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Popular >

expand ((1+r)/r)^2

Solution

expand

(\frac{1 + r}{r})^{2}

Solution

\frac{1}{r ^{2}} + \frac{2}{r} + 1

Solution steps

(\frac{1 + r}{r})^{2}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( 1 + r ) ^{2}}{r ^{2}}

(1 + r)^{2} = 1 + 2 r + r^{2}

= \frac{1 + 2 r + r ^{2}}{r ^{2}}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{1 + 2 r + r ^{2}}{r ^{2}} = \frac{1}{r ^{2}} + \frac{2 r}{r ^{2}} + \frac{r ^{2}}{r ^{2}}

= \frac{1}{r ^{2}} + \frac{2 r}{r ^{2}} + \frac{r ^{2}}{r ^{2}}

Apply rule

\frac{a}{a} = 1

\frac{r ^{2}}{r ^{2}} = 1

= \frac{1}{r ^{2}} + \frac{2 r}{r ^{2}} + 1

Cancel

\frac{2 r}{r ^{2}} : \frac{2}{r}

= \frac{1}{r ^{2}} + \frac{2}{r} + 1

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Frequently Asked Questions (FAQ)

What is expand ((1+r)/r)^2 ?
The solution to expand ((1+r)/r)^2 is 1/(r^2)+2/r+1