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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. 435R (page 561)

Multiply a polynomial by a monomial.
$a^{2} (a^{2} - 9 a - 36)$ .

Short Answer

Expert verified

The simplified form is $a^{4} - 9 a^{3} - 36 a^{2}$ .

Step by step solution

01

Step 1

Multiply $a^{2} (a^{2} - 9 a - 36)$ .

Use the distributive property $a (b + c) = a 路 b + a 路 c$ to perform the multiplication operation.

02

Step 2

Perform the multiplication operation:
$\begin{array}{rcl} a^{2} (a^{2} - 9 a - 36) & = & a^{2} 路 a^{2} + a^{2} (- 9 a) + a^{2} (- 36) \\ = & a^{4} - 9 a^{3} - 36 a^{2} \end{array}$

So, $a^{2} (a^{2} - 9 a - 36) = a^{4} - 9 a^{3} - 36 a^{2}$ .

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Most popular questions from this chapter

In the following exercises, find the product of ${(9 p + 8 q)}^{2}$ .

In the following exercises, multiply the binomials. Use any method.

$(x + 8) (x + 3)$

Multiply each pair of conjugates using the product of the conjugates pattern.

$(9 c + 5) (9 c - 5)$

Multiply each pair of conjugates using the product of the conjugates pattern.

$(8 j + 4) (8 j - 4)$

Solve the square using the binomial squares pattern.

${(x + \frac{2}{3})}^{2}$

See all solutions

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