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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 5: Q. 488 (page 564)

$(5 a^{2} + 2 a - 12) (9 a^{2} + 8 a - 4)$

Short Answer

Expert verified

The simplified form of the given expression is $45 a^{4} + 58 a^{3} - 112 a^{2} - 104 a + 48$ .

Step by step solution

01

Step 1. Given information.

The given expression is:

$(5 a^{2} + 2 a - 12) (9 a^{2} + 8 a - 4)$

02

Step 2. Simplify the given expression.

The given expression can be written as:

$= 5 a^{2} (9 a^{2} + 8 a - 4) + 2 a (9 a^{2} + 8 a - 4) - 12 (9 a^{2} + 8 a - 4) = 5 a^{2} (9 a^{2}) + 5 a^{2} (8 a) + 5 a^{2} (- 4) + 2 a (9 a^{2}) + 2 a (8 a) + 2 a (- 4) - 12 (9 a^{2}) - 12 (8 a) - 12 (- 4) = 45 a^{4} + 40 a^{3} - 20 a^{2} + 18 a^{3} + 16 a^{2} - 8 a - 108 a^{2} - 96 a + 48 = 45 a^{4} + (40 a^{3} + 18 a^{3}) + (- 20 a^{2} + 16 a^{2} - 108 a^{2}) + (- 8 a - 96 a) + 48 = 45 a^{4} + 58 a^{3} - 112 a^{2} - 104 a + 48$

03

Step 3. Conclusion.

The simplified form of the given expression is $45 a^{4} + 58 a^{3} - 112 a^{2} - 104 a + 48$ .

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Most popular questions from this chapter

Jennifer thinks the quotient $\frac{a^{24}}{a^{6}}$ simplifies to $a^{4}$ .What is wrong with her reasoning

Use the Factor Theorem to determine if $x + 3$ is a factor of $x^{3} + 8 x^{2} + 21 x + 18$ .

$(8 x^{3} + 6 x^{2}) 梅 2 x$

Using your own words, explain the difference between a monomial, a binomial, and a trinomial.

Simplify the expression.

$- 5^{- 3}$

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