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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. 184 (page 536)

In the following exercises, multiply.
$(a) - 8 y (y^{2} + 2 y - 15) (b) - 4 y^{2} z^{3} (3 y^{2} + 12 y z - z^{2})$

Short Answer

Expert verified

The solution is

$(a) - 8 y (y^{2} + 2 y - 15) = - 8 y^{3} - 16 y^{2} + 120 y (b) - 4 y^{2} z^{3} (3 y^{2} + 12 y z - z^{2}) = - 12 y^{4} z^{3} - 48 y^{3} z^{4} + 4 y^{2} z^{5}$

Step by step solution

01

Step 1. Apply the concept of Distributive Property

If $A, B a n d C$ are any real numbers or algebraic expressions, then

$A (B + C) = (B + C) A = A B + A C$

02

Part (a) Step 1. Given information

The given expression is

$- 8 y (y^{2} + 2 y - 15)$

03

Part (a) Step 2. Simplify

Using Distributive property,

$- 8 y (y^{2} + 2 y - 15) = - 8 y 路 y^{2} - 8 y 路 2 y + 8 y 路 15 = - 8 y^{3} - 16 y^{2} + 120 y$

04

Part (b) Step 1. Given information

The given expression is

$- 4 y^{2} z^{3} (3 y^{2} + 12 y z - z^{2})$

05

Part (b) Step 2. Simplify

Using Distributive property,

$- 4 y^{2} z^{3} (3 y^{2} + 12 y z - z^{2}) = - 4 y^{2} z^{3} 路 3 y^{2} - 4 y^{2} z^{3} 路 12 y z + 4 y^{2} z^{3} 路 z^{2} = - 12 y^{4} z^{3} - 48 y^{3} z^{4} + 4 y^{2} z^{5}$

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Most popular questions from this chapter

Simplify $\frac{{(- 4 m^{- 3})}^{2} {(5 m^{4})}^{3}}{{(- 10 m^{6})}^{3}}$

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

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