1. 7.3 Special Products

2. What We Will Learn Use square of a binomial pattern
Use sum and difference pattern

3. Ex. 1 Square of a Binomial 𝑎+𝑏 2 = 𝑎+𝑏 𝑎+𝑏 = 𝑎 2 +2𝑎𝑏+ 𝑏 2
𝑎+𝑏 2 = 𝑎+𝑏 𝑎+𝑏 = 𝑎 2 +2𝑎𝑏+ 𝑏 2
𝑎−𝑏 2 = 𝑎−𝑏 𝑎−𝑏 = 𝑎 2 −2𝑎𝑏+ 𝑏 2
If forget pattern, just use any method of multiplying learned before
FOIL, distribute, or table
Multiply:
3𝑥+4 2 = 3𝑥+4 3𝑥+4
a = 3x
b = 4
9𝑥 2 +24𝑥+16

4. Ex. 1 Cont. 5𝑥−2 2 Your Practice 5𝑥−2 5𝑥−2 7𝑥−3 2 25𝑥 2 −20𝑥+4
5𝑥−2 2
5𝑥−2 5𝑥−2
a = 5x
b = -2
25𝑥 2 −20𝑥+4
4𝑥+𝑦 2
4𝑥+𝑦 4𝑥+𝑦
a = 4x
b = 1y
16𝑥 2 +8𝑥𝑦+ 𝑦 2
Just put the two letter together in the middle
Your Practice
7𝑥−3 2
a = 7x
b = -3
49𝑥 2 −42𝑥+9
6𝑥+3𝑦 2
a = 6x
b = 3y
36𝑥 2 +36𝑥𝑦+ 9𝑦 2

5. Ex. 2 Sum and Difference Pattern
𝑎+𝑏 𝑎−𝑏 = 𝑎 2 − 𝑏 2
Multiply:
𝑡−5 𝑡+5
a = 1t
b = 5
𝑡 2 −25
2𝑥+3 2𝑥−3
a = 2x
b = 3
4𝑥 2 −9
2𝑥+3𝑦 2𝑥−3𝑦
a = 2x
b = 3y
4𝑥 2 − 9𝑦 2
Your Practice
𝑥+3 𝑥−3
𝑥 2 −9
𝑥+3𝑦 𝑥−3𝑦
𝑥 2 − 9𝑦 2

6. Ex. 3 Mental Math 26×34 16×24 20−4 20+4 Use difference of squares
Find number between both 30
Use difference of squares
30−
a = 30
b = 4
30 2 − 4 2
900-16
884
16×24 20
20−
a = 20
b = 4
20 2 − 4 2
400−16
384

7. Ex. 3 Cont. Your Practice 33×27 45 2 29 2 29×29 30−1 30−1
30−1 30−1
Use square of binomial pattern
𝑎 2 −2𝑎𝑏 + 𝑏 2
a = 30
b = -1
30 2 −2 30 −1 + −1 2
961
Your Practice
33×27 −3
900 – 9
891
45 2
45×45
2025