StudySmarter AI is coming soon!

- :00Days
- :00Hours
- :00Mins
- 00Seconds

A new era for learning is coming soonSign up for free

Suggested languages for you:

Americas

Europe

Q. 4

Expert-verifiedFound in: Page 395

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.

We have:

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

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

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

${\left(x+1\right)}^{2}={x}^{2}+2x\xb7\hspace{0.17em}1+{1}^{2}\phantom{\rule{0ex}{0ex}}={x}^{2}+2x+1$

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

Both sides are equal

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

94% of StudySmarter users get better grades.

Sign up for free