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

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1+k times \frac{4}{4}.

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

Since \frac{k^{2}}{4} and \frac{4\left(1+k\right)}{4} have the same denominator, add them by adding their numerators.

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

Do the multiplications in k^{2}+4\left(1+k\right).

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

Factor

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

Solution Steps

Factor out \frac{1}{4}.

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

Consider k^{2}+4+4k. Use the perfect square formula, a^{2}+2ab+b^{2}=\left(a+b\right)^{2}, where a=k and b=2.

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

Rewrite the complete factored expression.

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