展开 ((4x+5)^2)/(16)

解答

展开

\frac{( 4 x + 5 ) ^{2}}{16}

x^{2} + \frac{5 x}{2} + \frac{25}{16}

求解步骤

\frac{( 4 x + 5 ) ^{2}}{16}

(4 x + 5)^{2} = 16 x^{2} + 40 x + 25

= \frac{16 x ^{2} + 40 x + 25}{16}

使用分式法则:

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

\frac{16 x ^{2} + 40 x + 25}{16} = \frac{16 x ^{2}}{16} + \frac{40 x}{16} + \frac{25}{16}

= \frac{16 x ^{2}}{16} + \frac{40 x}{16} + \frac{25}{16}

数字相除:

\frac{16}{16} = 1

= x^{2} + \frac{40 x}{16} + \frac{25}{16}

消掉

\frac{40 x}{16} : \frac{5 x}{2}

= x^{2} + \frac{5 x}{2} + \frac{25}{16}

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