化简 (a-ib)(a+ib)^2

解答

化简

(a - ib) (a + ib)^{2}

(a^{3} + a b^{2}) + (a^{2} b + b^{3}) i

求解步骤

(a - ib) (a + ib)^{2}

= (a + ib)^{2} (a - ib)

展开

(a + ib)^{2} : a^{2} + 2 abi - b^{2}

= (a^{2} + 2 abi - b^{2}) (a - ib)

打开括号

= a^{2} a + a^{2} (- ib) + 2 abia + 2 abi (- ib) - b^{2} a - b^{2} (- ib)

化简

a^{2} a + a^{2} (- ib) + 2 abia + 2 abi (- ib) - b^{2} a - b^{2} (- ib) : a^{3} + a^{2} bi + a b^{2} + i b^{3}

= a^{3} + a^{2} bi + a b^{2} + i b^{3}

Rewrite in standard complex form:

(a^{3} + a b^{2}) + (a^{2} b + b^{3}) i

= (a^{3} + a b^{2}) + (a^{2} b + b^{3}) i

e x p an d \frac{18 y + 12}{( y - 6 ) ( y + 6 )}

e x p an d \frac{( y - 1 ) ^{4}}{y ^{\frac{1}{2}} ( y ^{2} + 1 ) ^{3}}

e x p an d \frac{1}{( X ^{2} + 8 ) ^{3}}

e x p an d (1 + tan (θ)) tan (2 θ)

e x p an d a (x + \frac{b}{2 a})^{2} - \frac{b ^{2}}{4 a} + c