展开 b(a+b+c)^3

解答

展开

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

b^{4} + 3 b^{3} a + 3 b^{3} c + 3 b^{2} a^{2} + 3 b^{2} c^{2} + 6 b^{2} a c + b a^{3} + b c^{3} + 3 ba c^{2} + 3 b a^{2} c

求解步骤

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

(a + b + c)^{3} = b^{3} + 3 b^{2} a + 3 b^{2} c + 3 b a^{2} + 3 b c^{2} + 6 ba c + a^{3} + c^{3} + 3 a c^{2} + 3 a^{2} c

= b (b^{3} + 3 b^{2} a + 3 b^{2} c + 3 b a^{2} + 3 b c^{2} + 6 ba c + a^{3} + 3 a^{2} c + 3 a c^{2} + c^{3})

打开括号

= b b^{3} + b \cdot 3 b^{2} a + b \cdot 3 b^{2} c + b \cdot 3 b a^{2} + b \cdot 3 b c^{2} + b \cdot 6 ba c + b a^{3} + b c^{3} + b \cdot 3 a c^{2} + b \cdot 3 a^{2} c

= b^{3} b + 3 b^{2} ba + 3 b^{2} b c + 3 bb a^{2} + 3 bb c^{2} + 6 bba c + b a^{3} + b c^{3} + 3 ba c^{2} + 3 b a^{2} c

化简

b^{3} b + 3 b^{2} ba + 3 b^{2} b c + 3 bb a^{2} + 3 bb c^{2} + 6 bba c + b a^{3} + b c^{3} + 3 ba c^{2} + 3 b a^{2} c : b^{4} + 3 b^{3} a + 3 b^{3} c + 3 b^{2} a^{2} + 3 b^{2} c^{2} + 6 b^{2} a c + b a^{3} + b c^{3} + 3 ba c^{2} + 3 b a^{2} c

= b^{4} + 3 b^{3} a + 3 b^{3} c + 3 b^{2} a^{2} + 3 b^{2} c^{2} + 6 b^{2} a c + b a^{3} + b c^{3} + 3 ba c^{2} + 3 b a^{2} c

e x p an d (x e^{x}) (1 + e^{x})

e x p an d e^{(1 - x^{2} - y^{2})} - 2 e^{(1 - x^{2} - y^{2})} x (x + y)

e x p an d \frac{4 x ^{2} - 4 x + 12}{x ( x + 3 ) ( x + 4 )}

\frac{d}{d q} ((r (q, x)) (12.5 + 0.02 x))

e x p an d ln (w + x) \cdot p + ln (w - x) \cdot (1 - p)