Lesson 74 MULTIPLY BINOMIAL BY TRINOMIAL.notebook
Aim: How do we multiply a binomial by a trinomial?
Do Now: Simplify each of the following:
1) 4x2 (2x2 + 3x ­ 8)
2) (2x ­ 5)(x + 4)
3) (4x2 +8) + (2x2 + 3x ­ 8)
4) (4x2 +8) ­ (2x2 + 3x ­ 8)
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Lesson 74 MULTIPLY BINOMIAL BY TRINOMIAL.notebook
Today we will be looking at multiplying a binomial by a trinomial.
ex) (3x2 + x ­ 5)(2x ­ 7)
Let's see if we can use our skills of multiplying two binomials to help us today!
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Lesson 74 MULTIPLY BINOMIAL BY TRINOMIAL.notebook
1) What is a simpler form of (3x2 + x ­ 5)(2x ­ 7)?
OPTION #1 VERTICAL METHOD Steps:
a) Multiply by arranging the polynomials vertically
3x2 + x ­ 5
2x ­ 7
b) Multiply by ­7 ­21x2 ­ 7x + 35
c) Multiply by 2x 6x3 + 2x2 ­ 10x
d) Add like terms 6x3 ­ 19x2 ­ 17x +35
OPTION #2 DISTRIBUTING METHOD(Triple Distribution)
a) Distribute each term from the binomial to each term in the trinomial.
(3x2 + x ­ 5)(2x ­ 7)
Commutative Property of multiplication allows you to change the order if you would like/need.
(2x ­ 7)(3x2 + x ­ 5)
6x3 + 2x2 ­ 10x ­ 21x2 ­ 7x + 35
b) Then combine like terms.
6x3 ­ 19x2 ­ 17x +35
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Lesson 74 MULTIPLY BINOMIAL BY TRINOMIAL.notebook
2) What is a simpler form of (2x2 ­ 3x + 1) (x ­ 3)?
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Lesson 74 MULTIPLY BINOMIAL BY TRINOMIAL.notebook
For each of the following, express in simplest form.
3) (x + 5) (x2 ­ 3x + 1)
5) (2a2 + 4a + 5)(5a ­ 4)
4) (k2 ­ 4k + 3)(k ­ 2)
6) (2g + 7)(3g2 ­ 5g + 2)
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Lesson 74 MULTIPLY BINOMIAL BY TRINOMIAL.notebook
7) (h + 2)(3h2 + h ­ 7)
8) (a ­ 1)(a2 ­ 4a + 9)
9) (2m ­3)(4m2 + 5m ­ 6)
10) (3x + 4) (2x2 ­ 6x ­ 3)
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Lesson 74 MULTIPLY BINOMIAL BY TRINOMIAL.notebook
CHALLENGE!!! SIMPLIFY THE FOLLOWING! 11) (p3 + 2p2 ­ 3)(p ­ 4)
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