展开 ((4y+1)^2)/(16)

解答

展开

\frac{( 4 y + 1 ) ^{2}}{16}

y^{2} + \frac{y}{2} + \frac{1}{16}

求解步骤

\frac{( 4 y + 1 ) ^{2}}{16}

(4 y + 1)^{2} = 16 y^{2} + 8 y + 1

= \frac{16 y ^{2} + 8 y + 1}{16}

使用分式法则:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{16 y ^{2} + 8 y + 1}{16} = \frac{16 y ^{2}}{16} + \frac{8 y}{16} + \frac{1}{16}

= \frac{16 y ^{2}}{16} + \frac{8 y}{16} + \frac{1}{16}

数字相除:

\frac{16}{16} = 1

= y^{2} + \frac{8 y}{16} + \frac{1}{16}

消掉

\frac{8 y}{16} : \frac{y}{2}

= y^{2} + \frac{y}{2} + \frac{1}{16}

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