化简 a^2*(b+c)-(b+c)^3

解答

化简

a^{2} \cdot (b + c) - (b + c)^{3}

a^{2} b + a^{2} c - b^{3} - 3 b^{2} c - 3 b c^{2} - c^{3}

求解步骤

a^{2} (b + c) - (b + c)^{3}

(b + c)^{3} : b^{3} + 3 b^{2} c + 3 b c^{2} + c^{3}

= a^{2} (b + c) - (b^{3} + 3 b^{2} c + 3 b c^{2} + c^{3})

乘开

a^{2} (b + c) : a^{2} b + a^{2} c

= a^{2} b + a^{2} c - (b^{3} + 3 b^{2} c + 3 b c^{2} + c^{3})

- (b^{3} + 3 b^{2} c + 3 b c^{2} + c^{3}) : - b^{3} - 3 b^{2} c - 3 b c^{2} - c^{3}

= a^{2} b + a^{2} c - b^{3} - 3 b^{2} c - 3 b c^{2} - c^{3}

e x p an d (x - y)^{3} + (x - y)^{2} + (x - y)

s im pl i f y \frac{( 4 a ^{4} - 8 a ^{2} \cdot b ^{2} + 4 b ^{4} )}{( a ^{2} \cdot b - b ^{3} )}

s im pl i f y (3 + 8) \cdot x^{6} - 42 - 7

f a c t or x^{7} y^{7} - x y

f a c t or 2 x^{2} - 3 x y - 2 y^{2}