展开 pi(3r+8s)^2*(12r+32s)

解答

展开

π (3 r + 8 s)^{2} \cdot (12 r + 32 s)

108 π r^{3} + 864 π r^{2} s + 2304 π r s^{2} + 2048 π s^{3}

求解步骤

π (3 r + 8 s)^{2} (12 r + 32 s)

使用分配律:

a (b + c) = ab + a c

a = π (3 r + 8 s)^{2}, b = 12 r, c = 32 s

= π (3 r + 8 s)^{2} \cdot 12 r + π (3 r + 8 s)^{2} \cdot 32 s

= 12 π r (3 r + 8 s)^{2} + 32 π s (3 r + 8 s)^{2}

化简

12 π r (3 r + 8 s)^{2} + 32 π s (3 r + 8 s)^{2} : 108 π r^{3} + 864 π r^{2} s + 2304 π r s^{2} + 2048 π s^{3}

= 108 π r^{3} + 864 π r^{2} s + 2304 π r s^{2} + 2048 π s^{3}

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