What is expand (iw+1)^3 ?

The solution to expand (iw+1)^3 is (-3w^2+1)+(-w^3+3w)i

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expand (iw+1)^3

expand

(i w + 1)^{3}

(- 3 w^{2} + 1) + (- w^{3} + 3 w) i

Solution steps

(i w + 1)^{3}

Apply Perfect Cube Formula:

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

(i w + 1)^{3} = (i w)^{3} + 3 (i w)^{2} \cdot 1 + 3 i w \cdot 1^{2} + 1^{3}

= (i w)^{3} + 3 (i w)^{2} \cdot 1 + 3 i w \cdot 1^{2} + 1^{3}

Simplify

(i w)^{3} + 3 (i w)^{2} \cdot 1 + 3 i w \cdot 1^{2} + 1^{3} : - w^{3} i - 3 w^{2} + 3 w i + 1

= - w^{3} i - 3 w^{2} + 3 w i + 1

Rewrite in standard complex form:

(- 3 w^{2} + 1) + (- w^{3} + 3 w) i

= (- 3 w^{2} + 1) + (- w^{3} + 3 w) i

\frac{( x + 6 ) ^{2}}{x + 8}

\frac{1}{( x + 1 ) ( x ^{2} + 1 ) ^{2}}

(x^{2} - 2) y d x

(2 - \frac{1}{2} x)^{10}

\frac{1}{2} - \frac{( w - 1 ) ^{2}}{2} + 2 w - 2 - \frac{w ^{2} - 1}{2}

What is expand (iw+1)^3 ?
The solution to expand (iw+1)^3 is (-3w^2+1)+(-w^3+3w)i