Solve (k+1)^2(1+2k+3/(k+1)^2)

$$( k + 1 ) ^ { 2 } ( 1 + \frac { 2 k + 3 } { ( k + 1 ) ^ { 2 } } )$$

Evaluate

$$\left(k+2\right)^{2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{\left(k+1\right)^{2}}{\left(k+1\right)^{2}}.

$$\left(k+1\right)^{2}\left(\frac{\left(k+1\right)^{2}}{\left(k+1\right)^{2}}+\frac{2k+3}{\left(k+1\right)^{2}}\right)$$

Since \frac{\left(k+1\right)^{2}}{\left(k+1\right)^{2}} and \frac{2k+3}{\left(k+1\right)^{2}} have the same denominator, add them by adding their numerators.

$$\left(k+1\right)^{2}\times \frac{\left(k+1\right)^{2}+2k+3}{\left(k+1\right)^{2}}$$

Do the multiplications in \left(k+1\right)^{2}+2k+3.

$$\left(k+1\right)^{2}\times \frac{k^{2}+2k+1+2k+3}{\left(k+1\right)^{2}}$$

Combine like terms in k^{2}+2k+1+2k+3.

$$\left(k+1\right)^{2}\times \frac{k^{2}+4k+4}{\left(k+1\right)^{2}}$$

Cancel out \left(k+1\right)^{2} and \left(k+1\right)^{2}.

$$k^{2}+4k+4$$

Expand

$$k^{2}+4k+4$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{\left(k+1\right)^{2}}{\left(k+1\right)^{2}}.

$$\left(k+1\right)^{2}\left(\frac{\left(k+1\right)^{2}}{\left(k+1\right)^{2}}+\frac{2k+3}{\left(k+1\right)^{2}}\right)$$

Since \frac{\left(k+1\right)^{2}}{\left(k+1\right)^{2}} and \frac{2k+3}{\left(k+1\right)^{2}} have the same denominator, add them by adding their numerators.

$$\left(k+1\right)^{2}\times \frac{\left(k+1\right)^{2}+2k+3}{\left(k+1\right)^{2}}$$

Do the multiplications in \left(k+1\right)^{2}+2k+3.

$$\left(k+1\right)^{2}\times \frac{k^{2}+2k+1+2k+3}{\left(k+1\right)^{2}}$$

Combine like terms in k^{2}+2k+1+2k+3.

$$\left(k+1\right)^{2}\times \frac{k^{2}+4k+4}{\left(k+1\right)^{2}}$$

Cancel out \left(k+1\right)^{2} and \left(k+1\right)^{2}.

$$k^{2}+4k+4$$