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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q5.52 (page 1069)

Multiply : (a) $4 x^{2} (2 x^{2} - 3 x + 5)$
(b) $- 6 a^{3} b (3 a^{2} - 2 a b + 6 b^{2})$

Short Answer

Expert verified

$(a) B y m u l t i p l y t h e b i n o m i a l s u \sin g D i s t r i b u t i v e p r o p e r t y, w e g e t 4 x^{2} (2 x^{2} - 3 x + 5) 8 x^{4} - 12 x^{3} + 20 x^{2} (b) B y m u l t i p l y t h e b i n o m i a l s u \sin g d i s t r i b u t i v e p r o p e r t y, w e g e t - 6 a^{3} b (3 a^{2} - 2 a b + 6 b^{2}) - 18 a^{5} b + 12 a^{4} b^{2} - 36 a^{3} b^{3}$

Step by step solution

01

Step 1

Given Information:

(a) $4 x^{2} (2 x^{2} - 3 x + 5)$

(b) $- 6 a^{3} b (3 a^{2} - 2 a b + 6 b^{2})$

02

Step 2

Distributive Property;

Distributive Property is an algebraic property that is used to multiply a single value and two or more values within a set of parenthesis.

03

Step 3Part(a) Step1. Multiply the binomials

(a) $4 x^{2} (2 x^{2} - 3 x + 5)$

Distribute: $4 x^{2} 脳 2 x^{2} + 4 x^{2} 脳 (- 3 x) + 4 x^{2} 脳 5$

Multiply: $8 x^{4} - 12 x^{3} + 20 x^{2}$

04

Step 4Part(b) Step1. Multiply the binomials

(b) $- 6 a^{3} b (3 a^{2} - 2 a b + 6 b^{2})$

Distribute: $- 6 a^{3} b 脳 3 a^{2} + (- 6 a^{3} b) 脳 (- 2 a b) + (- 6 a^{3} b) 脳 6 b^{2}$

Multiply: $- 18 a^{5} b + 12 a^{4} b^{2} - 36 a^{3} b^{3}$

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