Product of Two Binomials (FOIL Method)

MATHEMATICS 8
Patterns and Algebra (1st Quarter)
SPECIAL
PRODUCTS
MR. CARLO JUSTINO J. LUNA
Subject Teacher

MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) MR. CARLO JUSTINO J. LUNA
WARM UP
Simplify.
𝟓 𝟐
Answer: 𝟐𝟓

WARM UP
Simplify.
𝟖 𝟐
Answer: 𝟔𝟒

WARM UP
Simplify.
(−𝟑) 𝟐
Answer: 𝟗

WARM UP
Simplify.
(𝒚) 𝟐
Answer: 𝒚 𝟐

WARM UP
Simplify.
−(𝟓𝒂) 𝟐
Answer: −𝟐𝟓𝒂 𝟐

WARM UP
Simplify.
(𝒃 𝟑
) 𝟐
Answer: 𝒃 𝟔

WARM UP
Simplify.
𝟐(𝟒𝒂𝒃)
Answer: 𝟖𝒂𝒃

WARM UP
Simplify.
−𝟑(𝟓𝒙 𝟐
)
Answer: −𝟏𝟓𝒙 𝟐

WARM UP
Simplify.
𝟐(𝟕𝒙 + 𝟏)
Answer: 𝟏𝟒𝐱 + 𝟐

WARM UP
Simplify.
−𝟓(𝟐𝒂 + 𝒃)
Answer:
−𝟏𝟎𝐚 − 𝟓𝐛

WARM UP
Simplify.
x(𝟑𝒙 − 𝒚)
Answer:
𝟑𝒙 𝟐
− 𝐱𝐲

WARM UP
Simplify.
𝟐𝒂𝒃(𝟒𝒂 + 𝟑𝒃)
Answer:
𝟖𝒂 𝟐
𝒃 + 𝟔𝒂𝒃 𝟐

How about
𝒙 + 𝟐 𝟐𝒙 + 𝟑
?
GOOD JOB!

The Distributive Property
𝒙 + 𝟐 𝟐𝒙 + 𝟑
𝒙 𝟐𝒙 + 𝟑 + 𝟐(𝟐𝒙 + 𝟑)
𝟐𝒙 𝟐
+ 𝟑𝒙 + 𝟒𝒙 + 𝟔
𝟐𝒙 𝟐
+ 𝟕𝒙 + 𝟔
NOTE: Since there are THREE terms,
this is called a TRINOMIAL.

You try!
𝟐𝒙 − 𝟓 𝟐𝒙 − 𝟏
𝟐𝒙 𝟐𝒙 − 𝟏 − 𝟓(𝟐𝒙 − 𝟏)
𝟒𝒙 𝟐
− 𝟐𝒙 − 𝟏𝟎𝒙 + 𝟓
𝟒𝒙 𝟐
− 𝟏𝟐𝒙 + 𝟓

 Multiplying MOST binomials results in
THREE terms
TRINOMIALS
 You can learn to
multiply binomials in
your head by using a
method called
F O I L

 The FOIL method is ONLY used when you
multiply two (2) binomials.
 It is an acronym and tells you which terms to
multiply.
FOIL
 Use the FOIL method
to multiply the
following binomials:
(𝑦 + 4)(𝑦 + 5)

F tells you to multiply the FIRST
terms of each binomial.
(𝒚 + 𝟒)(𝒚 + 𝟓)
𝒚 𝟐

O tells you to multiply the OUTER
(𝒚 + 𝟒)(𝒚 + 𝟓)
𝒚 𝟐
+ 𝟓𝒚

I tells you to multiply the INNER
(𝒚 + 𝟒)(𝒚 + 𝟓)
𝒚 𝟐
+ 𝟓𝒚 + 𝟒𝒚

L tells you to multiply the LAST
(𝒚 + 𝟒)(𝒚 + 𝟓)
𝒚 𝟐
+ 𝟓𝒚 + 𝟒𝒚 + 𝟐𝟎

(𝒚 + 𝟒)(𝒚 + 𝟓)
𝒚 𝟐
+ 𝟓𝒚 + 𝟒𝒚 + 𝟐𝟎
Combine LIKE terms.
𝒚 𝟐
+ 𝟓𝒚 + 𝟒𝒚 + 𝟐𝟎
𝒚 𝟐
+ 𝟗𝒚 + 𝟐𝟎

FOIL reminds you to
multiply the:
First terms
Outer terms
Inner terms
Last terms
REMEMBER…

1. (3𝑎 + 7)(𝑎 − 3)
2. 5𝑥 − 1 2𝑥 − 5
3. 𝑚 + 2𝑛 𝑚 + 𝑛
4. 4𝑚 − 9 2𝑚 + 1
5. (𝑥2
+ 3𝑥)(2𝑥2
− 5𝑥)
YOU TRY!

The 2nd method is the BOX method. This
method works for every problem!
Here’s how you do it:
(𝟒𝒙– 𝟑)(𝟐𝒙 + 𝟓)
Draw a box. Write a polynomial on
the top & side of a box.
It does not matter where.
This will be modeled in the next
problem along with FOIL.
𝟒𝒙 −𝟑
𝟐𝒙
+𝟓

Multiply (𝟒𝒙 − 𝟑)(𝟐𝒙 + 𝟓)
First terms:
Outer terms:
Inner terms:
Last terms:
Combine like terms.
𝟖𝒙 𝟐 + 𝟏𝟒𝒙– 𝟏𝟓
4𝒙 −𝟑
2𝒙
+5
𝟖𝒙 𝟐
+𝟐𝟎𝒙
−𝟔𝒙
−𝟏𝟓
You have 2 techniques. Pick the one you like the best!
𝟖𝒙 𝟐
+𝟐𝟎𝒙
−𝟔𝒙
−𝟏𝟓

Multiply (𝟕𝒂 + 𝟓)(𝟑𝒂 − 𝟏)
First terms:
Outer terms:
Inner terms:
Last terms:
Combine like terms.
𝟐𝟏𝒂 𝟐 + 𝟖𝒂 − 𝟓
𝟕𝒂 +𝟓
𝟑𝒂
−𝟏
𝟐𝟏𝒂 𝟐
−𝟕𝒂
+𝟏𝟓𝒂
−𝟓
𝟐𝟏𝒂 𝟐
−𝟕𝒂
+𝟏𝟓𝒂
−𝟓

Multiply (𝟐𝒎 + 𝒏)(𝟒𝒎 + 𝟐𝒏)
First terms:
Outer terms:
Inner terms:
Last terms:
Combine like terms.
𝟖𝒎 𝟐 + 𝟖𝒎𝒏 + 𝟐𝒏 𝟐
𝟐𝒎 +𝒏
𝟒𝒎
+𝟐𝒏
𝟖𝒎 𝟐
𝟒𝒎𝒏
𝟒𝒎𝒏
𝟐𝒏 𝟐
𝟖𝒎 𝟐
+𝟒𝒎𝒏
+𝟒𝒎𝒏
𝟐𝒏 𝟐

EASY Round
1 point
AVERAGE Round
3 points
DIFFICULT Round
5 points

−𝟓𝒙(𝟕𝒙)
Answer:
−𝟑𝟓𝒙 𝟐
EASY
1 point

𝟒𝒃(𝟔𝒃 𝟑
)
Answer:
𝟐𝟒𝒃 𝟒
EASY
1 point

−𝟑𝒚 𝟐
(−𝟕𝒚 𝟓
)
Answer:
𝟐𝟏𝒚 𝟕
EASY
1 point

𝟐𝒙(𝒙 + 𝟒)
Answer:
𝟐𝒙 𝟐
+ 𝟖𝒙
EASY
1 point

𝟐(𝟑𝒙 𝟐
+ 𝟒𝒙 − 𝟏)
Answer:
𝟔𝒙 𝟐
+ 𝟖𝒙 − 𝟐
EASY
1 point

(𝟐𝒙 + 𝟏)(𝒙 + 𝟏)
Answer:
𝟐𝒙 𝟐
+ 𝟑𝒙 + 𝟏
AVERAGE
3 points

(𝟑𝒂 + 𝟑)(𝟐𝒂 − 𝟒)
Answer:
𝟔𝒂 𝟐
− 𝟔𝒂 − 𝟏𝟐
AVERAGE
3 points

(𝟓𝒏 − 𝟓)(𝟑𝒏 + 𝟕)
Answer:
𝟏𝟓𝒏 𝟐
+ 𝟐𝟎𝒏 − 𝟑𝟓
AVERAGE
3 points

(𝟐𝒃 − 𝟏)(𝟒𝒃 − 𝟑)
Answer:
𝟖𝒃 𝟐
− 𝟏𝟎𝒃 + 𝟑
AVERAGE
3 points

−𝟑 (𝟐𝒙 − 𝟐)(𝟑𝒙 + 𝟒)
Answer:
−𝟏𝟖𝒙 𝟐
− 𝟔𝒙 + 𝟐𝟒
DIFFICULT
5 points

𝟐𝒂 (𝟓𝒂 + 𝟑)(𝟑𝒂 − 𝟐)
Answer:
−𝟑𝟎𝒂 𝟑
− 𝟐𝒂 𝟐
− 𝟏𝟐𝒂
DIFFICULT
5 points

−𝒂 𝟐
(𝟒𝒂 𝟐
− 𝟑𝒂)(𝟐𝒂 𝟐
− 𝒂)
Answer:
−𝟖𝒂 𝟔
+ 𝟏𝟎𝒂 𝟓
− 𝟑𝒂 𝟒
DIFFICULT
5 points

MATHEMATICS 8
Patterns and Algebra (1st Quarter)
THANK YOU!
MR. CARLO JUSTINO J. LUNA
Subject Teacher

Product of Two Binomials (FOIL Method)

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