展开 (((2p+q)^3-(q-2p)^3))/(2p)

解答

展开

\frac{( ( 2 p + q ) ^{3} - ( q - 2 p ) ^{3} )}{2 p}

8 p^{2} + 6 q^{2}

求解步骤

\frac{( 2 p + q ) ^{3} - ( q - 2 p ) ^{3}}{2 p}

分解

(2 p + q)^{3} - (q - 2 p)^{3} : 4 p ((2 p + q)^{2} + (2 p + q) (q - 2 p) + (q - 2 p)^{2})

= \frac{4 p ( ( 2 p + q ) ^{2} + ( 2 p + q ) ( q - 2 p ) + ( q - 2 p ) ^{2} )}{2 p}

消掉

\frac{4 p ( ( 2 p + q ) ^{2} + ( 2 p + q ) ( q - 2 p ) + ( q - 2 p ) ^{2} )}{2 p} : 2 ((2 p + q)^{2} + (2 p + q) (q - 2 p) + (q - 2 p)^{2})

= 2 ((2 p + q)^{2} + (2 p + q) (q - 2 p) + (q - 2 p)^{2})

乘开

(2 p + q)^{2} + (2 p + q) (q - 2 p) + (q - 2 p)^{2} : 4 p^{2} + 3 q^{2}

= 2 (4 p^{2} + 3 q^{2})

使用分配律:

a (b + c) = ab + a c

a = 2, b = 4 p^{2}, c = 3 q^{2}

= 2 \cdot 4 p^{2} + 2 \cdot 3 q^{2}

化简

2 \cdot 4 p^{2} + 2 \cdot 3 q^{2} : 8 p^{2} + 6 q^{2}

= 8 p^{2} + 6 q^{2}

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