Solve 1/4k^2(k^2+2k+1)+(k^3+3k^2+3k+1)

$$\frac { 1 } { 4 } k ^ { 2 } ( k ^ { 2 } + 2 k + 1 ) + ( k ^ { 3 } + 3 k ^ { 2 } + 3 k + 1 )$$

Evaluate

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

Solution Steps

Use the distributive property to multiply \frac{1}{4}k^{2} by k^{2}+2k+1.

$$\frac{1}{4}k^{4}+\frac{1}{2}k^{3}+\frac{1}{4}k^{2}+k^{3}+3k^{2}+3k+1$$

Combine \frac{1}{2}k^{3} and k^{3} to get \frac{3}{2}k^{3}.

$$\frac{1}{4}k^{4}+\frac{3}{2}k^{3}+\frac{1}{4}k^{2}+3k^{2}+3k+1$$

Combine \frac{1}{4}k^{2} and 3k^{2} to get \frac{13}{4}k^{2}.

$$\frac{1}{4}k^{4}+\frac{3}{2}k^{3}+\frac{13}{4}k^{2}+3k+1$$

Expand

$$\frac{k^{4}}{4}+\frac{3k^{3}}{2}+\frac{13k^{2}}{4}+3k+1$$

Solution Steps

Use the distributive property to multiply \frac{1}{4}k^{2} by k^{2}+2k+1.

$$\frac{1}{4}k^{4}+\frac{1}{2}k^{3}+\frac{1}{4}k^{2}+k^{3}+3k^{2}+3k+1$$

Combine \frac{1}{2}k^{3} and k^{3} to get \frac{3}{2}k^{3}.

$$\frac{1}{4}k^{4}+\frac{3}{2}k^{3}+\frac{1}{4}k^{2}+3k^{2}+3k+1$$

Combine \frac{1}{4}k^{2} and 3k^{2} to get \frac{13}{4}k^{2}.

$$\frac{1}{4}k^{4}+\frac{3}{2}k^{3}+\frac{13}{4}k^{2}+3k+1$$