簡約 (1/2 a-b)^2

解

簡約

(\frac{1}{2} a - b)^{2}

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

解答ステップ

(\frac{1}{2} a - b)^{2}

\frac{1}{2} a = \frac{a}{2}

= (\frac{a}{2} - b)^{2}

完全平方式を適用する:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

a = \frac{a}{2}, b = b

= (\frac{a}{2})^{2} - 2 \cdot \frac{a}{2} b + b^{2}

簡素化

(\frac{a}{2})^{2} - 2 \cdot \frac{a}{2} b + b^{2} : \frac{a ^{2}}{4} - ab + b^{2}

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