Solve 4x^2+2xy+y^2/4

$$4 x ^ { 2 } + 2 x y + \frac { y ^ { 2 } } { 4 }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4x^{2}+2xy times \frac{4}{4}.

$$\frac{4\left(4x^{2}+2xy\right)}{4}+\frac{y^{2}}{4}$$

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

$$\frac{4\left(4x^{2}+2xy\right)+y^{2}}{4}$$

Do the multiplications in 4\left(4x^{2}+2xy\right)+y^{2}.

$$\frac{16x^{2}+8xy+y^{2}}{4}$$

Factor

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

Solution Steps

Factor out \frac{1}{4}.

$$\frac{16x^{2}+8xy+y^{2}}{4}$$

Consider 16x^{2}+8xy+y^{2}. Use the perfect square formula, a^{2}+2ab+b^{2}=\left(a+b\right)^{2}, where a=4x and b=y.

$$\left(4x+y\right)^{2}$$

Rewrite the complete factored expression.

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