Transcript Lesson 5.10

Bellringer
Multiply the following using the FOIL
method
1.
(2x – 4)(2x + 4)
4𝑥 2 − 16
2.
(3y + 5)(3y + 5)
9𝑦 2 + 30𝑦 + 25
5.10 Multiplying Binomials:
Special Products
Use FOIL to multiply.
(x + 2)(x – 2)
𝑥 ∙ 𝑥 + 𝑥 ∙ −2 + 2 ∙ 𝑥 + 2 ∙ −2
2
𝑥 − 2𝑥 + 2𝑥 − 4
2
𝑥 −4
Product of sum and difference of
same two terms
(A + B)(A – B) = A2 – B2
Square of the first minus square of
the second
Multiply.
(r + 2)(r – 2)
2
2
𝑟 −2
2
𝑟 −4
Multiply.
(2x + 3)(2x – 3)
2
2
(2𝑥) −3
2
2
2
2 𝑥 −3
2
4𝑥 − 9
Multiply.
(2x3 + y)(2x3 – y)
3
2
2
(2𝑥 ) − 𝑦
2
3
2
2
2 ∙ 𝑥
−𝑦
6
2
4𝑥 − 𝑦
Multiply.
(y6 – y2)(y6 + y2)
6
2
2
2
(𝑦 ) − (𝑦 )
12
4
𝑦 −𝑦
Squaring a Binomial
Multiply the binomial by itself
Multiply.
(x +
2
2)
= (x + 2)(x + 2)
𝑥∙𝑥+2∙𝑥+2∙𝑥+2∙2
2
𝑥
+ 2𝑥 + 2𝑥 + 4
2
𝑥 + 4𝑥 + 4
Multiply.
(3x + 5)2 = (3x + 5)(3x + 5)
3𝑥 ∙ 3𝑥 + 3𝑥 ∙ 5 + 5 ∙ 3𝑥 + 5 ∙ 5
2
9𝑥 + 15𝑥 + 15𝑥 + 25
2
9𝑥
+ 30𝑥 + 25
Multiply.
(3x – 5y)2 = (3x – 5y)(3x – 5y)
3𝑥 ∙ 3𝑥 + 3𝑥 ∙ −5𝑦 − 5𝑦 ∙ 3𝑥 − 5𝑦 ∙ −5𝑦
2
9𝑥 − 15𝑥𝑦 − 15𝑥𝑦 + 25𝑦
2
9𝑥 − 30𝑥𝑦 + 25𝑦
2
2
Squaring a Binomial
(A + B)2 = A2 + 2AB + B2
(A - B)2 = A2 – 2AB + B2
Multiply
(5𝑥 − 2𝑦)2
(5𝑥)2 −2 ∙ 5𝑥 ∙ 2𝑦 + (2𝑦)2
52 ∙ 𝑥 2 − 2 ∙ 5 ∙ 2 ∙ 𝑥 ∙ 𝑦 + 22 ∙ 𝑦 2
25𝑥 2 − 20𝑥𝑦 + 4𝑦 2
Multiply
(6𝑥 2 𝑦 − 4𝑥)2
(6𝑥 2 𝑦)2 −2 ∙ 6𝑥 2 𝑦 ∙ 4𝑥 + (4𝑥)2
62 𝑥 4 𝑦 2 − 48𝑥 3 𝑦 + 16𝑥 2
36𝑥 4 𝑦 2 − 48𝑥 3 𝑦 + 16𝑥 2
Multiply
(2𝑦 3 − 4𝑥)2
(2𝑦 3 )2 −2 ∙ 2𝑦 3 ∙ 4𝑥 + 4𝑥
22 𝑦 6 − 16𝑥𝑦 3 + 42 𝑥 2
4𝑦 6 − 16𝑥𝑦 3 + 16𝑥 2
2
Assignment