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Expert-verified Found in: Page 395 ### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465 # The equation ${x}^{2}+2x={\left(x+1\right)}^{2}-1$ is an identity.

The statement "The equation ${x}^{2}+2x={\left(x+1\right)}^{2}-1$ is an identity" is true.

See the step by step solution

## Step 1. Given information.

We have:

${x}^{2}+2x={\left(x+1\right)}^{2}-1$

## Step 2. Find whether the statement is true or false.

The equation is ${x}^{2}+2x={\left(x+1\right)}^{2}-1$.

Apply perfect square formula: ${\left(a+b\right)}^{2}={a}^{2}+2ab+{b}^{2}$

${\left(x+1\right)}^{2}={x}^{2}+2x· 1+{1}^{2}\phantom{\rule{0ex}{0ex}}={x}^{2}+2x+1$

${x}^{2}+2x={x}^{2}+2x+1-1\phantom{\rule{0ex}{0ex}}{x}^{2}+2x={x}^{2}+2x\phantom{\rule{0ex}{0ex}}0=0$

Both sides are equal

Therefore, the statement "the equation ${x}^{2}+2x={\left(x+1\right)}^{2}-1$ is identity" is true. ### Want to see more solutions like these? 