化简 [ 1/4a-1/2b+1]^2

解答

化简

[\frac{1}{4} \cdot a - \frac{1}{2} \cdot b + 1]^{2}

\frac{- ab + b ^{2}}{4} + \frac{a ^{2}}{16} + \frac{a}{2} - b + 1

求解步骤

(\frac{1}{4} a - \frac{1}{2} b + 1)^{2}

\frac{1}{4} a = \frac{a}{4}

\frac{1}{2} b = \frac{b}{2}

= (\frac{a}{4} - \frac{b}{2} + 1)^{2}

(\frac{a}{4} - \frac{b}{2} + 1)^{2} = (\frac{a}{4} - \frac{b}{2} + 1) (\frac{a}{4} - \frac{b}{2} + 1)

= (\frac{a}{4} + 1 - \frac{b}{2}) (\frac{a}{4} + 1 - \frac{b}{2})

乘开

(\frac{a}{4} - \frac{b}{2} + 1) (\frac{a}{4} - \frac{b}{2} + 1) : \frac{- ab + b ^{2}}{4} + \frac{a ^{2}}{16} + \frac{a}{2} - b + 1

= \frac{- ab + b ^{2}}{4} + \frac{a ^{2}}{16} + \frac{a}{2} - b + 1

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