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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 7: Q 277. (page 868)

Explain why $n^{2} + 25 鈮� {(n + 5)}^{2}$ . Use algebra, words, or pictures.

Short Answer

Expert verified

It is explained by an algebraic procedure that the expressions are not equal for every $n .$

Step by step solution

01

The given information

The given expression is $n^{2} + 25 鈮� {(n + 5)}^{2} .$

02

Ex[lanation the given problem.

Square the expression:

${(n + 5)}^{2} = n^{2} + 2 路 n 路 5 + 5^{2} = n^{2} + 10 n + 25 .$

This shows that $n^{2} + 25 鈮� n^{2} + 10 n + 25 鈬� n^{2} + 25 鈮� {(n + 5)}^{2} .$

Expressions are not equal when $n$ is not zero, so it follows that the only solution where the expressions are equal is when $n$ is zero.

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