Solve (x-1)^2(x-3i)(x+3i)

$$( x - 1 ) ^ { 2 } ( x - 3 i ) ( x + 3 i )$$

Evaluate

$$\left(x-1\right)^{2}\left(x^{2}+9\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

$$\left(x^{2}-2x+1\right)\left(x-3i\right)\left(x+3i\right)$$

Use the distributive property to multiply x^{2}-2x+1 by x-3i and combine like terms.

$$\left(x^{3}+\left(-2-3i\right)x^{2}+\left(1+6i\right)x-3i\right)\left(x+3i\right)$$

Use the distributive property to multiply x^{3}+\left(-2-3i\right)x^{2}+\left(1+6i\right)x-3i by x+3i and combine like terms.

$$x^{4}-2x^{3}+10x^{2}-18x+9$$

Expand

$$x^{4}-2x^{3}+10x^{2}-18x+9$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

$$\left(x^{2}-2x+1\right)\left(x-3i\right)\left(x+3i\right)$$

Use the distributive property to multiply x^{2}-2x+1 by x-3i and combine like terms.

$$\left(x^{3}+\left(-2-3i\right)x^{2}+\left(1+6i\right)x-3i\right)\left(x+3i\right)$$

Use the distributive property to multiply x^{3}+\left(-2-3i\right)x^{2}+\left(1+6i\right)x-3i by x+3i and combine like terms.

$$x^{4}-2x^{3}+10x^{2}-18x+9$$