Solve a^2/4-ab+b^2

$$\frac { a ^ { 2 } } { 4 } - a b + b ^ { 2 }$$

Evaluate

$$\frac{\left(a-2b\right)^{2}}{4}$$

Short Solution Steps

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

$$\frac{a^{2}}{4}+\frac{4\left(-ab+b^{2}\right)}{4}$$

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

$$\frac{a^{2}+4\left(-ab+b^{2}\right)}{4}$$

Do the multiplications in a^{2}+4\left(-ab+b^{2}\right).

$$\frac{a^{2}-4ab+4b^{2}}{4}$$

Factor

$$\frac{\left(a-2b\right)^{2}}{4}$$

Solution Steps

Factor out \frac{1}{4}.

$$\frac{a^{2}-4ab+4b^{2}}{4}$$

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

$$\left(a-2b\right)^{2}$$

Rewrite the complete factored expression.

$$\frac{\left(a-2b\right)^{2}}{4}$$