The four steps for evaluating expressions are: 1) Simplify expressions within parentheses 2) Perform exponent operations 3) Multiply and divide from left to right 4) Add and subtract from left to right These steps follow the order of operations known as PEDMAS (Parentheses, Exponents, Division/Multiplication, Addition/Subtraction). The key is to follow the proper order to correctly simplify complex expressions.

1. Based on the readings and content for this course.docx
Based on the readings and content for this course, which topic
did you find most useful or interesting? How will you use it
later in life? What makes it valuable?
Ans:
Well, there are many small but significant things in real life,
that I understand, are related to maths.
For example the screen size of a TV or a laptop. When we say
14 inch laptop we mean the diagonal of the screen is
approximately 14 inches.
This is a direct application of Pythagorean Theorem.
And depending on the shape of the room determines the formula
for area that I use. For example, if our room was a perfect
square (which none of them are) I would utilize the formula a =
s^2, since our rooms our rectangle, the formula we more
commonly use is a = lw.
Again I understand the amount of money we spend on gas can
be modeled by a mathematical function.
When we throw a ball up, the time taken for it to come down
can be modeled by a quadratic equation.
There are so many things.
I won't pick up any particular thing.
But after this course, I am able to look at many things in a more
analytical way.
I can understand the mathematical logic behind them.
So all these are valuable to me

2. Do you always use the property of distribution when
multiplying monomials and polynomials.docx
Do you always use the property of distribution when
multiplying monomials and polynomials? Explain why or why
not. In what situations would distribution become important?
Provide an example for the class to practice with.
Ans:
The property of distribution is one important tool in solving the
polynomial multiplications.
For example:
3x*(x+5) = 3x*x + 3x*5 = 3x^2 +15x
But this property is used only when one of the bracketed terms
contains two or more terms of different order.
For example in the above case, the bracket consists of two
different order terms, x and 5.
Let’s take another case:
3x*(x+2x)
This can be solved in two ways.
3x(x+2x) = 3x*x + 3x*2x = 3x^2 +6x^2 = 9x^2
Or we can say:
3x(x+2x) = 3x*3x = 9x^2

3. So in the 1st method we used the distribute property.
But in the 2nd case we did not.
So it depends on the particular problem and looking at the
different terms we can decide whether or not to use distributive
property.
Explain how to factor the following trinomials forms.docx
Explain how to factor the following trinomials forms: x2 + bx +
c and ax2 + bx + c. Is there more than one way to factor this?
Show your answer using both words and mathematical notation
Ans:
Actually I am not very sure how to answer this.
For me x2 + bx + c and ax2 + bx + c are not different from each
other.
The 1st one is a special case of the second expression where
a=1.
To factor the expression ax^2 + bx + c we first need to factor
the middle term bx cleverly.
Now it's to be understood that not all trinomials can be factored.
But some of them can be.
Basically, we have to write b in the form b= p+q so that p*q=
a*c. This is the only trick.
Then we can just take out the common factors.
Let's see through an example.
Example 1:
x^2 + 2x +1
Here a=1 , b=2 and c=2

4. So the product a*c = 1*1 =1
We write b= 2= 1+1 so their product is also 1*1=1
So x^2 + 2x +1
= x^2 + x+ x +1
= x(x+1) + 1(x+1)
= (x+1)(+1)
Example -2:
4x^2 + 12x + 9
= 4x^2 + 6x + 6x +9
= 2x (2x+3) + 3 (2x+3)
=(2x+3)(2x+3)
Example -3 :
x^2 + 15x + 54
= x^2 + 9x + 6x + 54
= x (x+9) + 6 (x+9)
=(x+6)(x+9)
Explain the five steps for solving rational equations.docx
Explain the five steps for solving rational equations. Can any of
these steps be eliminated? Can the order of these steps be
changed? Would you add any steps to make it easier, or to make
it easier to understand?
The 5 steps for solving a rational equation are as follows,
1) First of all we determine the least common denominator

5. (LCD) of the terms associated with the equation
2) Then multiply each side of the equation by the LCD
3) Then simplify each term
4) Now solve the final equation
5) Then put the answers in the original equation to make a
check.
I am not very sure which part I can omit or skip.
I will go through what others have written
Then I can have a better understanding I hope.
Explain the four steps for solving quadratic equations.docx
Explain the four steps for solving quadratic equations. Can any
of these steps be eliminated? Can the order of these steps be
changed? Would you add any steps to make it easier, or to make
it easier to understand?
There may be different ways to solve quadratic equations.
For example one can use factoring or one may use quadratic
formula.
For me quadratic formula is the best way to solve any quadratic
equation.
The steps involved may be as follows:
Let’s consider the quadratic equation of the form : ax^2 + bx +
c= 0
The first step will be to identify the coefficients a,b and c.
The second step will be to calculate the discriminant D= b^2 –
4ac.
The 3rd step may be to check the value of D.
If D > 0 then we have two real solutions.
If D < 0 then we have two imaginary solutions.
If D=0 then we have one real solution.

6. The last step will be to put the value in the quadratic formula
and simplify to get the values of x.
X= [-b ± SQRT (b^2 – 4ac)]/ 2a
I think we can skip the 2nd and 3rd step. Once we identify the
values of a, b and c, we can simply use the quadratic formula to
get the results.
From the concepts you have learned in this course.docx
From the concepts you have learned in this course, provide a
real-world application of something that you think has been the
most valuable to you? Why has it been valuable?
Answer 1:
As silly as it may seem, what I am finding that has been of the
most benefit to me is one of the more basic properties that we
learned. And that was back in our second or third week of the
course when we started looking into the properties how to
measure area of a square or rectangle. The reason that I have
found this information to be so beneficial to me is because we
are doing home renovations. And when we make trips to Lowe's
for materials such as flooring, it is measured in squared footage.
So for me to know how many boxes of flooring we need to buy,
I first need to know the dimensions of the room that we are
covering. And depending on the shape of the room determines
the formula for area that I use. For example, if our room was a
perfect square (which none of them are) I would utilize the
formula a = s^2, since our rooms our rectangle, the formula we
more commonly use is a = lw.

7. Answer 2:
Well, there are many small but significant things in real life,
that I understand, are related to maths.
For example the screen size of a TV or a laptop. When we say
14 inch laptop we mean the diagonal of the screen is
approximately 14 inches.
This is a direct application of Pythagorean Theorem.
Similarly the area of square floor. Again I understand the
amount of money we spend on gas can be modeled by a
mathematical function.
When we throw a ball up, the time taken for it to come down
can be modeled by a quadratic equation.
There are so many things.
I won't pick up any particular thing.
But after this course, I am able to look at many things in a more
analytical way.
I can understand the mathematical logic behind them.
How are these concepts of direct.docx
How are these concepts of direct, inverse, and joint variation
used in everyday life? Provide examples for each.
ans
These are some of the concepts which I can visualize in daily
life.
The concepts of direct, inverse and joint variation are used a lot
in daily life although we may not notice it.

8. Let’s see them by some simple examples.
Direct variation:
Suppose 1 ice-cream costs $10. So 10 ice-creams will cost $100.
This is a simple example of direct variations.
We can find many more examples of this.
Indirect variation:
Suppose one person takes 40 minutes to do complete a work.
Then how much will 4 persons take to complete the work
together.
The answer is 4 persons will take 10 minutes to complete it.
This is an example of inverse variation.
Joint Variation:
Mathematically, we can say that if x varies directly with y and
if x varies inversely with z then we can write:
x= K y/z
where K is a constant.
So this is a joint variation.
But right now I cannot remember a real life application.
I will go through fellow students’ answers.
I can get some idea from there.
How do you factor the difference of two squares.docx
How do you factor the difference of two squares? How do you
factor the perfect square trinomial? How do you factor the sum
and difference of two cubes? Which of these three makes the
most sense to you? Explain why.
How do you factor the difference of two squares?
This is my personal favorite and I guess this one is the easiest
of them all to factor.
If we have somthing like a^2 - b^2, then we can factor it out
like:
a^2 - b^2 = (a+b)(a-b)
For example :

9. Factor: 16a^2 - 9
16a^2 - 9
= (4a)^2 - 3^2
= (4a+3)(4a-3)
How do you factor the perfect square trinomial?
The only trick in this kind of trinomials is to identify that this is
a perfect square.
It has to be in the form a^2 + 2*a*b + b^2 (or a^2 -2*a*b +
b^2).
Then it's easy to write it as (a+b)^2 or (a-b)^2
For example:
4x^2 + 12x + 9
=(2x)^2 + 2*2a*3 +3^2
=(2x+3)^2
How do you factor the sum and difference of two cubes?
When we have a sum of two cubes we can factor it as :
a^3 + b^3 = (a+b)(a^2 -ab +b^2)
Similarly, if we have a difference of two cubes, then we can
write it as:
a^3 - b^3 = (a-b)(a^2 +ab+b^2)
I hope I have done them all correctly.
If your neighbor asked you to explain what you learned in this
course.docx

10. If your neighbor asked you to explain what you learned in this
course, what would you tell her?
Well. It will be a bit difficult for me to explain to someone what
I learned through this class.
There are so many things and I am not very sure how to explain
all these things to a lay man.
I can give example of a few things, like how to find the area of
a wall or a flooring or how to calculate the speed.
I can try to explain about the negative integers. I can tell them
how the speed of a car is calculated.
There are so many things which I can tell them. But then there
are some things which are difficult to explain for me.
It will be difficult to explain the quadratic equations or the
radicals
Other than those listed in the text how might the Pythagorean
theorem be used in everyday life.docx
Other than those listed in the text how might the Pythagorean
theorem be used in everyday life? Provide examples of each.
Well this is one more concept which I understand has a lot of
applications in daily life although we may not know this
exactly.
The best example that comes to mind is the regarding the TV
screens.
When we talk about a 21" TV we actually mean the diagonal of
the screen is 21" which comes from the Pythagorean theorem.
Same is the case for laptops.
I think carpenters also use these principles a lot in their
profession.
Also when we use a ladder to reach at a certain height of a wall,

11. it’s the
Pythagorean theorem which comes into play.
For example suppose we need to reach a height of 8 meters of a
wall.
And we can place the ladder at 6 meters from the wall.
So the minimum length of the ladder must be
SQRT(62+82)=SQRT(36+64)=SQRT(100)=10 meters.
Right now I cannot come up with anymore example.
But I will search and come up with more
Quadratic equations, which are expressed in the form.docx
Quadratic equations, which are expressed in the form of ax2 +
bx + c = 0, where a does not equal 0, may have how many
solutions? Explain why.
Ans:
Any quadratic equation of the form ax^2 + bx +c =0 can have at
most two solutions.
I am not sure how to explain this.
As I understand the maximum number of solution of any
equation equals the highest power of x in that equation.
In case of a quadratic equation, the discriminant D=b2 - 4ac,
tells us how many real number solutions the equation ax2 + bx
+ c= 0 has.
When D = negative, has two non real imaginary number
solutions.
When D = 0, it has only one solution, it is a real number b/c
zero is the perfect square and can be factored as a square
When D = positive it has two different real number solutions
This is as much as I understand.

12. I will look at other answers to know more.
What are the two steps for simplifying radicals.docx
What are the two steps for simplifying radicals? Can either step
be deleted? If you could add a step that might make it easier or
easier to understand, what step would you add?
The following steps should be taken to simplify a radical
expression:
step 1 - First the largest perfect nth power factor of the radicand
must be found.
step 2 - Then factor out and simplify the perfect nth power.
We look at this with a simple example:
I am considering square root for simplicity.
√24 + √54
= √(4*6) + √(9*6) (Write 24 = 4*6 = 2*2*6 and 54 = 9*6 =
3*3*6)
= 2√6 + 3√6 (√4 = and √9 =3)
= √6 (2+3) (Factoring out √6)
= 5√6
What constitutes a rational expression.docx
What constitutes a rational expression? How would you explain
this concept to someoneunfamiliar with it?
Ans:
A rational expression is an expression which has variables in
both the numerator and/or denominator. It’s a kind of fraction
with polynomials

13. In case of a rational expression we have to make sure that the
denominator is not equal to 0 because division by zero is not
allowed. Anything divided by zero is undefined.
In 3x/(x^2 - 16), the value of x can't be -4 or 4, since it makes
the denominator equal to 0
When we explain this to someone, first of all I should explain
what is a fraction.
For example : 2/3 is a fraction or x/y is a fration.
In case of x/y, x is numerator and y is denominator.
If we replace x and y by expressions like: (2x+5)/(3x-8), it
becomes a rational expression.
What four steps should be used in evaluating expressions.docx
We need to apply the PEDMAS rule for this.
Step's are:
Step 1:Parenthesis or brackets solved first. There are three types
of parenthesis [ ],{},( ). The order of them is ( ) first then { }
and at the last [ ].
Step 2: Exponential, if there is any exponential terms as a^x in
the brackets then we need to simplify that.
Step 3:D-> Division and M--> Multiplication we need to
perform them from left to right if they both are present in the
same expression under same brackets.
Step 4:A--> Addition and S--> Subtraction. We need to perform
them from left to right if they both are present in the same
expression under same brakets.We first need to solve ( )
expression and then { } expression and then [ ] at the last.

14. We can skip some of these steps if there is no need of them.
Like if there is no term of exponential including then no need to
apply that step. In the same way we can skip some steps only if
they are not present in the question
What is the greatest common factor.docx
What constitutes a rational expression? How would you explain
this concept to someone unfamiliar with it?
A rational expression is an expression which has variables in
both the numerator and/or denominator. It’s a kind of fraction
with polynomials
We have to make sure that the denominator is not equal to 0
because division by zero is not allowed. Anything divided by
zero is undefined.
For example 3x/(x^2 - 16) is a rational expression.
Here 3x is the numerator and x^2-16 is the denominator.
Again here, value of x can't be -4 or 4, since it makes the
denominator equal to 0.
What is the quadratic formula.docx
What is the quadratic formula? What is it used for? Provide a
useful example, not found in the text.
The quadratic formula is used to solve quadratic equations.
It is one of the best tools to solve any quadratic equation.
Suppose we consider an equation of the form : ax^2 + bx + c =0
Then the quadratic formula says that we can give the solutions
as :

15. X= [-b ± SQRT (b^2 – 4ac)]/ 2a
Let's consider an example:
x^2 + 4x +4 =0
Solve for x.
Here a= 1, bn=4 and c=4.
So putting in the formula we get:
x= [-b ± SQRT (b^2 – 4ac)]/ 2a
=[-4 ± SQRT (4^2 – 4*1*4)]/ 2*1
=[-4 ± SQRT (16 – 16)]/ 2
= -4/2
=-2
So the solution is x=-2
What is the relationship between exponents and logarithms.docx
What is the relationship between exponents and logarithms?
How would you distinguish between the two? Provide an
example for the class to practice translating between the two.
Ans:
For me again this is a tricky question to answer.
I will try to explain it as I understand it.
When we mean exponents I understand something like ax = b.
This is an exponential notation.
Here a is the base and x is the exponent.
The above equation can be represented in a different way as:
x = loga b
This is called a logarithmic representation.

16. Example:
Consider the following exponential : 102 = 100
This can be written in logarithmic notation as: log10 100 =2
Problem for class:
Covert the following exponential to logarithim.
25=32
What one area from the readings in Week Three are you most
comfortable with.docx
What one area from the readings in Week Three are you most
comfortable with? Why do you think that is? Using what you
know about this area, create a discussion question that would
trigger a discussion—that is, so there is no single correct
answer to the question
Well. I must say it's a bit difficult to answer this question.
I am not very sure which part do I like most.
But I guess I like the concept of factoring expressions which are
in the form of difference of two squares.
For example : a^2 - b^2 = (a+b)(a-b)
I also like to factor the expressions which are in the form of a^2
+ 2ab + b^2 so that we can write them in the form
a^2 + 2ab + b^2 = (a+b)^2
But I like these two because they are easy to done. The best part
as per me is to factor a trinomial where we have to split the
middle term and then factor it out. I love that concept
What role do radical numbers play in your current or future

17. profession.docx
What role do radical numbers play in your current or future
profession? Provide a specific example and relate your
discussion to your classroom learning this week.
Ans:
I do not really know how this concept of radicla number can fit
into aby day to day proffesion.
As far as I understand, this will have more use in science and
technology.
Banking proffesionals may have a use of it.
Also perhaps architects might be using it.
Other than this I do not know how this concepts come into play
in other proffesions.
I will look into others’ responses to have a clue.
Which of the four operations on functions do you think is the
easiest to perform.docx
Which of the four operations on functions do you think is the
easiest to perform? What is the most difficult? Explain why.
If I am correct we are talking about the four operations which
are addition, subtraction, multiplication and division.
When talking of functions, these operations becomes
complicated as compared to normal variables.
But for me I thing addition is the easiest one and also
subtraction.
The multiplication and division may be a bit more difficult.
I will look at what other fellow classmates are talking about and
try to learn more on this.
Which of the special products are you most comfortable with
and why.docx

18. Which of the special products are you most comfortable with
and why? Using what you know about this special product,
create an example for the class to practice factoring.
Ans:
For me the factoring of difference of two squares is the most
comfortable one.
First of all it is easier to recognize a square as compared to a
cube.
And the corresponding factor is also so simple.
a^2 - b^2 = (a+b)(a-b)
I don't see any other formula so simple.
Let's see an example:
16x^2 -9y^2 = (4x)^2 - (3y)^2 = (4x+3y)(4x-3y)
Let's consider a difference of cubes.
8x^3 - 27 = (2x)^3 - 3^3 = (2x-3)(4x^2+6x+9)
For me the first one was definitely easier to identify and solve.
Why is scientific notation so important in today.docx
Why is scientific notation so important in today's society? Find
a practical use of scientific notation and share it with the class
as well as your thoughts as to why it was vital in this situation.
Ans:
Scientifics notations give us a proper and better way to
represent very large or very small numbers.

19. For example, 450000 can be written as : 4.5 * 105.
Since 450000 is a small number we don’t realize the importance
of scientific notation.
Consider the number 4500000000000000000000.
It will be a cumbersome job to write or use this number.
Instead we can write this as: 4.5*1020.
This makes our life much easier if we want to use this number.
I think the scientific notations have a lot of use in science and
engineering.
I searched on internet to find a good use of this and I found an
interesting application.
The distance between the Sun and the Earth is almost d=15*107
km
Speed of light is c = 3 *105 km/s
So time taken for light to reach on Earth from Sun is: t= d/c =
15*107/3*105
= (15/3)*102
= 5*102 sec
=500 sec
= 8 min 20 sec
Now if we have to do this calculation without scientific
notations, it will be very difficult.
Write a word problem involving a quadratic function.docx
Write a word problem involving a quadratic function. How
would you explain the steps in finding the solution to someone
not in this class?
I searched through internet and found the relation for a free
falling body.

20. So I made this problem myself.
Hope this will work.
Word Problem:
The distance traveled by a free falling body under the action of
gravity is given by the relation:
h=(1/2)gt^2
where h is the height
g is the acceleration due to gravity = 9.8 m/s^2
and t is the time taken.
Suppose a stone is dropped from a height of 10 meters.
Find the time taken to reach the ground.
Solution
:
From the equation we can find the time as:
h=(1/2)gt^2
or t^2 = 2h/g
or t = sqrt (2h/g) [we do not consider the negative root as time
cannot be negative]

21. or t = sqrt (2*10/9.8) = sqrt(20/9.8) = 1.42 sec
I hope I have done it correctly.
Please let me know if I made any mistakes.