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Q. 4

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Precalculus Enhanced with Graphing Utilities

Found in: Page 395

Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

The equation $x^{2} + 2 x = {(x + 1)}^{2} - 1$ is an identity.

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

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

We have:

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

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

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

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

${(x + 1)}^{2} = x^{2} + 2 x \cdot 1 + 1^{2} = x^{2} + 2 x + 1$

$x^{2} + 2 x = x^{2} + 2 x + 1 - 1 x^{2} + 2 x = x^{2} + 2 x 0 = 0$

Both sides are equal

Therefore, the statement "the equation $x^{2} + 2 x = {(x + 1)}^{2} - 1$ is identity" is true.

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