algebra class 8 chapter 10 icse

1. ALGEBRAIC EXPRESSIONS &
IDENTITIES
CHAPTER 10

2. WHY WE NEED TO STUDY ALGEBRA?
• https://www.youtube.com/watch?v=w0b7N3n78Ok
• https://www.youtube.com/watch?v=NybHckSEQBI

3. • Algebraic Expressions- Algebraic expression is a
collection or combination of constant and variables of one or
more terms, which are separated by fundamental operations
• Terms- various parts of an algebraic expressions separated
by + or – signs are called Terms.
• Constant- A term of an algebraic expression which has a
fixed numerical value and does not have any variable is called
constant term of the expression.
• Variables- Variables are represented by letters of the English
alphabet like x, y, z, a, b, c etc.
• Co-efficient- In a term of an algebraic expression, each of
the factors with the sign of the term is called a coefficient of the
product of the factors.

4. ALGEBRAIC EXPRESSIONS

6. ALGEBRAIC EXPRESSIONS

7. ALGEBRAIC
EXPRESSION
1. MONOMIAL: AN ALGEBRAIC EXPRESSION WHICH CONSISTS OF ONLY ONE
NON-ZERO TERM IS CALLED MONOMIAL. FOR EXAMPLE, 3Y
2. BINOMIAL: AN ALGEBRAIC EXPRESSION WHICH CONSISTS OF TWO NON-
ZERO TERM IS CALLED BINOMIAL. FOR EXAMPLE, 3X + Y
3. TRINOMIAL: AN ALGEBRAIC EXPRESSION WHICH CONSISTS OF THREE
NON-ZERO TERM IS CALLED TRINOMIAL. FOR EXAMPLE, 2A2 + 5A – 4
4. POLYNOMIAL: AN ALGEBRAIC EXPRESSION WHICH CONSISTS OF ONE,
TWO, THREE OR MORE NON-ZERO TERMS IS CALLED POLYNOMIAL. FOR
EXAMPLE,
2A2 + 5A – 4, 5M3 + 2M2 + 8M + 7 ETC
DEGREE OF A POLYNOMIAL: THE DEGREE OF A POLYNOMIAL IS THE HIGHEST
POWER OF ITS VARIOUS TERMS. FOR EXAMPLE, 2X2 – 3X5 + 5X6 , DEGREE
OF THE POLYNOMIAL IS 6

8. • https://www.youtube.com/watch?v=hd-QRfRx2Zc

10. ADDITION OF POLYNOMIAL
• Horizontal Method:
• Add 5x + 3y, 4x – 4y + z and -3x + 5y + 2z
= (5x + 3y) + (4x – 4y + z) + (-3x + 5y + 2z)
= 5x + 3y + 4x – 4y + z – 3x + 5y + 2z
= 5x + 4x – 3x + 3y – 4y + 5y + z + 2z
= 6x + 4y 3z
Vertical Method:- Add 7a + 5b, 6a – 6b + 3c, and -5a + 7b + 4c
= 7a + 5b
6a – 6b + 3c
- 5a + 7b + 4c
8a + 6b + 7c

11. SUBTRACTION OF POLYNOMIAL
• Horizontal Method: Subtract 2x – 5y + 3z from 5x + 9y – 2z
• = 5x + 9y – 2z – (2x – 5y + 3z)
• = 5x + 9y – 2z – 2x + 5y – 3z
• = 5x – 2x + 9y + 5y – 2z – 3z
• = 3x + 14y – 5z
• Vertical Method: Subtract : x – 4y -2z from 7x -3y + 6z
• = 7x – 3y + 6z
• x – 4y – 2z
• (-) (+) (+)
• = 6x + y + 8z

12. TEST ZONE
• 1. Add the following
• (a) 3xyz + 4yz + 5zx, 7xz – 6yz + 4xyz and – 9xyz – 11zy +
9xz
• (b) 9x2 – 7x + 5, - 14x2 – 6 + 15x and 20x2 + 40x – 17
2. Find the difference
(a) 4ab + 6bc – 8ca from 6ab – 3bc – 3ca + 11abc
(b) 5 – x -4y + 4z from 5x – 7y + 2z
3. what must be added to 1- 2x + 3x2 to obtain 3 + 5x – 7x2 ?
4. From the sum of 4b2 + 5bc , - 2b2 – 2bc – 2z2 and 2bc + 4c2 ,
Subtract the sum of 5b2 – c and – 3b2 + 2bc + c2 ?

14. MULTIPLY POLYNOMIALS USING DISTRIBUTIVE
PROPERTY

15. MULTIPLY POLYNOMIALS USING FOIL METHOD

16. MULTIPLY BY RECTANGLE METHOD

17. MULTIPLY BY VERTICAL METHOD

18. MULTIPLICATION OF POLYNOMIAL
• Binomial by a Trinomial-
• Find the product of (9ab – 3)(ab2 – 4b +7a)
• = 9ab(ab2 – 4b +7a) – 3(ab2 – 4b +7a)
• = 9a2b3 – 36ab2 + 63a2b – 3ab2 + 12b – 21a
• = 9a2b3 – 36ab2 – 3ab2 + 63a2b + 12b – 21a
• = 9a2b3 – 39ab2 + 63a2b + 12b – 21a
• Trinomial by a trinomial-
• Find the product (a2 + 2ab + b2)(a2 – 2ab + b2)
• = = a2(a2 – 2ab + b2) + 2ab(a2 – 2ab + b2) + b2 (a2 – 2ab + b2 )
• = a4 – 2a3b + a2b2 + 2a3b – 4a2b2 + 2ab3 + a2b2 – 2ab2 + b4
• = a4 + a2b2 – 4a2b2 + a2b2 + b4
• = a4 – 2a2b2 + b4

19. DIVISION OF
ALGEBRAIC
EXPRESSIONS

20. DIVISION ALGORITHM
•Dividend = Divisor x Quotient + Remainder
•N = d*q + r

21. DIVISION
•Division of monomial by a monomial
•Division of polynomial by a monomial
•Division of polynomial by a polynomial

22. DIVISION OF MONOMIAL BY A MONOMIAL
•xm ÷ xn = x m-n
•Example:

23. POLYNOMIAL
_______
MONOMIAL

24. DIVISION OF POLYNOMIAL BY A POLYNOMIAL

25. DIVISION OF POLYNOMIAL
• Divide: (3x2 + x – 1) ÷ (x + 1)
•

26. DIVISION OF POLYNOMIALS

28. DIVISION OF POLYNOMIALS

29. TEST ZONE

30. ALGEBRAIC IDENTITIES
• https://www.youtube.com/watch?v=Ygkzh4sJOQE

31. Proving Algebraic
Identity Expansion
Geometrically
In this section, we are going to see,
how to prove the expansions of
algebraic identities geometrically.
Let us consider algebraic identity and
its expansion given below.
(a + b)2 = a2 + 2ab + b2
We can prove the the expansion of (a
+ b)2 using the area of a square as
shown below.

33. GEOMETRIC PROOF OF IDENTITY 3: a2 – b2 = (a+b) (a-b)
• Geometric proof of (a+b) (a-b)

34. ALGEBRAIC IDENTITIES
• (a + b)2 = a2 + 2ab + b2
• (a - b)2 = a2 - 2ab + b2
• (a + b)(a - b) = a2 – b2
• (x + a)(x – b) = x2 + (a + b)x + ab

35. APPLICATION OF IDENTITIES
• (a + b)2 = a2 + 2ab + b2

36. APPLICATION OF IDENTITIES
• (a - b)2 = a2 - 2ab + b2

37. APPLICATION OF IDENTITIES
• (a + b)(a - b) = a2 – b2

38. APPLICATION OF IDENTITIES
• (x + a)(x – b) = x2 + (a + b)x + ab