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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. 182 (page 536)

In the following exercises, multiply.
$(a) - 8 x (x^{2} + 2 x - 15) (b) 5 p q^{3} (p^{2} - 2 p q + 6 q^{2})$

Short Answer

Expert verified

The solution is

$(a) - 8 x (x^{2} + 2 x - 15) = - 8 x^{3} - 16 x^{2} + 120 x (b) 5 p q^{3} (p^{2} - 2 p q + 6 q^{2}) = 5 p^{3} q^{3} - 10 p^{2} q^{4} + 30 p q^{5}$

Step by step solution

01

Step 1. Apply the concept of Distributive Property

If $A, B, C$ are any real number or algebraic expressions then

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

02

Part (a) Step 1. Given expression

The given expression is

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

03

Part (a) Step 2. Simplify

Using Distributive property ,

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

04

Part (b) Step 1. Given information

The given expression is

$5 p q^{3} (p^{2} - 2 p q + 6 q^{2})$

05

Part (b) Step 2. Simplify

Using Distributive property,

$5 p q^{3} (p^{2} - 2 p q + 6 q^{2}) = 5 p q^{3} 路 p^{2} - 5 p q^{3} 路 2 p q + 5 p q^{3} 路 6 q^{2} = 5 p^{3} q^{3} - 10 p^{2} q^{4} + 30 p q^{5}$

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Most popular questions from this chapter

Solve the square using the binomial squares pattern.

${(8 p^{3} - 3)}^{2}$

In the following exercises, multiply the binomials using a) the Distributive Property; b) the FOIL method; c) the Vertical Method

$(4 p + 11) (5 p - 4)$

Write number (a) 8,750,000 (b) 0.00000871 in scientific notation

Multiply: (a) $(5 y^{7}) (- 7 y^{4})$

(b) $(\frac{2}{5} a^{4} b^{3}) (15 a b^{3})$ .

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

$(p + \frac{4}{5} q) (p - \frac{4}{5} q)$

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