Page 592 - Algebra 1

Example
2
Multiply S_OLUTION
_2_
= 48m2n+12mn
= 2mn(4m+1) · 15 ____
_ Multiplying a Rational Expression by a Polynomial 2
9 ·(x -2x-15).Simplifyyouranswer. 3x - 15
Write the polynomial with a denominator of1.
Factor the trinomial.
Divide out like factors.
Simplify. Distribute.
Math Reasoning
Justify How did you decide what binomials to factor the trinomial into?
2
9 ·(x -2x-15)
3x - 15
= 9 · (x2 -2x-15)
___ 3x - 15 1
= 9 · (x-5)(x+3) _ _ _
3(x - 5) 1
= 9 · (x-5)(x+3)
_3 __
3(x - 5) 1
= 3(x + 3) = 3x + 9
1
There is more than one way to find the product of two rational expressions. The factors can be multiplied first before being simplified. Another way to solve the problem would be to simplify each expression first, and then to multiply, simplifying again if necessary.
. Simplify your answer.
Example
3
_2 __ Multiply 8m n + 2mn · 15
Multiplying Rational Expressions Containing Polynomials
2m 24mn + 6n Method 1: Multiply first.
SOLUTION
8mn+2mn · 15 8mn+2mn · 15 _2 __ _2 __
2m 24mn + 6n 2m
= 15(8mn+2mn) = 2mn(4m+1) · 15
24mn + 6n _2_ ____
2m(24mn + 6n) 120m n + 30mn
2m 6n(4m + 1) 1 5
Method 2: Factor first.
2 m 62 n ( 4 m + 1 ) =30mn(4m+1) _5 1
_ _ 12mn(4m + 1)
= 2
30mn(4m + 1) __
5
= 12mn(4m + 1) 2
= _5 2
Lesson 88 577