simplify (x+2i)^3

Solution

simplify

(x + 2 i)^{3}

(x^{3} - 12 x) + (6 x^{2} - 8) i

Solution steps

(x + 2 i)^{3}

Apply Perfect Cube Formula:

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

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

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

3 x^{2} \cdot 2 i = 6 x^{2} i

3 x (2 i)^{2} = - 12 x

(2 i)^{3} = - 8 i

= x^{3} + 6 x^{2} i - 12 x - 8 i

Rewrite in standard complex form:

(x^{3} - 12 x) + (6 x^{2} - 8) i

= (x^{3} - 12 x) + (6 x^{2} - 8) i

\frac{2 ( x ^{4} - 3 x ^{2} )}{( x ^{2} - 1 ) ^{2}}

\frac{1}{( 3 + n ) ^{2}}

5 (y - 10 = - 5)

2 (5 + 8)