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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.457R (page 561)

In the following exercises, square each binomial using the Binomial Squares Pattern.
${(5 p + 7 q)}^{2}$ .

Short Answer

Expert verified

The solution is ${(5 p + 7 q)}^{2} = 25 p^{2} + 70 p q + 49 q^{2}$ .

Step by step solution

01

Step 1

Recall the Binomial Squares Patterns:

${(a + b)}^{2} = a^{2} + 2 a b + b^{2} {(a - b)}^{2} = a^{2} - 2 a b + b^{2}$

02

Step 2

Use ${(a + b)}^{2} = a^{2} + 2 a b + b^{2}$ to find ${(5 p + 7 q)}^{2}$ .

$\begin{array}{rcl} {(5 p + 7 q)}^{2} & = & {(5 p)}^{2} + 2 (5 p) (7 q) + {(7 q)}^{2} \\ = & 25 p^{2} + 70 p q + 49 q^{2} \end{array}$

So, ${(5 p + 7 q)}^{2} = 25 p^{2} + 70 p q + 49 q^{2}$ .

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