Solve b^2/4-b+1

$$\frac { b ^ { 2 } } { 4 } - b + 1$$

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

Factor

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

Solution Steps

Factor out \frac{1}{4}.

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

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

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

Rewrite the complete factored expression.

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