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

$$( x + 1 ) ( x - ( 3 - 2 i ) ) ( x - ( 3 + 2 i ) )$$

Evaluate

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

Solution Steps

Use the distributive property to multiply x+1 by x-\left(3-2i\right).

$$\left(x\left(x-\left(3-2i\right)\right)+x-\left(3-2i\right)\right)\left(x-\left(3+2i\right)\right)$$

Use the distributive property to multiply x\left(x-\left(3-2i\right)\right)+x-\left(3-2i\right) by x-\left(3+2i\right).

$$x\left(x-\left(3-2i\right)\right)\left(x-\left(3+2i\right)\right)+\left(x-\left(3-2i\right)\right)\left(x-\left(3+2i\right)\right)$$

Multiply -1 and 3-2i to get -3+2i.

$$x\left(x+\left(-3+2i\right)\right)\left(x-\left(3+2i\right)\right)+\left(x-\left(3-2i\right)\right)\left(x-\left(3+2i\right)\right)$$

Multiply -1 and 3+2i to get -3-2i.

$$x\left(x+\left(-3+2i\right)\right)\left(x+\left(-3-2i\right)\right)+\left(x-\left(3-2i\right)\right)\left(x-\left(3+2i\right)\right)$$

Use the distributive property to multiply x by x+\left(-3+2i\right).

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

Apply the distributive property by multiplying each term of x^{2}+\left(-3+2i\right)x by each term of x+\left(-3-2i\right).

$$x^{3}+\left(-3-2i\right)x^{2}+\left(-3+2i\right)x^{2}+13x+\left(x-\left(3-2i\right)\right)\left(x-\left(3+2i\right)\right)$$

Combine \left(-3-2i\right)x^{2} and \left(-3+2i\right)x^{2} to get -6x^{2}.

$$x^{3}-6x^{2}+13x+\left(x-\left(3-2i\right)\right)\left(x-\left(3+2i\right)\right)$$

Multiply -1 and 3-2i to get -3+2i.

$$x^{3}-6x^{2}+13x+\left(x+\left(-3+2i\right)\right)\left(x-\left(3+2i\right)\right)$$

Multiply -1 and 3+2i to get -3-2i.

$$x^{3}-6x^{2}+13x+\left(x+\left(-3+2i\right)\right)\left(x+\left(-3-2i\right)\right)$$

Apply the distributive property by multiplying each term of x+\left(-3+2i\right) by each term of x+\left(-3-2i\right).

$$x^{3}-6x^{2}+13x+x^{2}+\left(-3-2i\right)x+\left(-3+2i\right)x+13$$

Combine \left(-3-2i\right)x and \left(-3+2i\right)x to get -6x.

$$x^{3}-6x^{2}+13x+x^{2}-6x+13$$

Combine -6x^{2} and x^{2} to get -5x^{2}.

$$x^{3}-5x^{2}+13x-6x+13$$

Combine 13x and -6x to get 7x.

$$x^{3}-5x^{2}+7x+13$$

Expand

$$x^{3}-5x^{2}+7x+13$$

Solution Steps

Use the distributive property to multiply x+1 by x-\left(3-2i\right).

$$\left(x\left(x-\left(3-2i\right)\right)+x-\left(3-2i\right)\right)\left(x-\left(3+2i\right)\right)$$

Use the distributive property to multiply x\left(x-\left(3-2i\right)\right)+x-\left(3-2i\right) by x-\left(3+2i\right).

$$x\left(x-\left(3-2i\right)\right)\left(x-\left(3+2i\right)\right)+\left(x-\left(3-2i\right)\right)\left(x-\left(3+2i\right)\right)$$

Multiply -1 and 3-2i to get -3+2i.

$$x\left(x+\left(-3+2i\right)\right)\left(x-\left(3+2i\right)\right)+\left(x-\left(3-2i\right)\right)\left(x-\left(3+2i\right)\right)$$

Multiply -1 and 3+2i to get -3-2i.

$$x\left(x+\left(-3+2i\right)\right)\left(x+\left(-3-2i\right)\right)+\left(x-\left(3-2i\right)\right)\left(x-\left(3+2i\right)\right)$$

Use the distributive property to multiply x by x+\left(-3+2i\right).

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

Apply the distributive property by multiplying each term of x^{2}+\left(-3+2i\right)x by each term of x+\left(-3-2i\right).

$$x^{3}+\left(-3-2i\right)x^{2}+\left(-3+2i\right)x^{2}+13x+\left(x-\left(3-2i\right)\right)\left(x-\left(3+2i\right)\right)$$

Combine \left(-3-2i\right)x^{2} and \left(-3+2i\right)x^{2} to get -6x^{2}.

$$x^{3}-6x^{2}+13x+\left(x-\left(3-2i\right)\right)\left(x-\left(3+2i\right)\right)$$

Multiply -1 and 3-2i to get -3+2i.

$$x^{3}-6x^{2}+13x+\left(x+\left(-3+2i\right)\right)\left(x-\left(3+2i\right)\right)$$

Multiply -1 and 3+2i to get -3-2i.

$$x^{3}-6x^{2}+13x+\left(x+\left(-3+2i\right)\right)\left(x+\left(-3-2i\right)\right)$$

Apply the distributive property by multiplying each term of x+\left(-3+2i\right) by each term of x+\left(-3-2i\right).

$$x^{3}-6x^{2}+13x+x^{2}+\left(-3-2i\right)x+\left(-3+2i\right)x+13$$

Combine \left(-3-2i\right)x and \left(-3+2i\right)x to get -6x.

$$x^{3}-6x^{2}+13x+x^{2}-6x+13$$

Combine -6x^{2} and x^{2} to get -5x^{2}.

$$x^{3}-5x^{2}+13x-6x+13$$

Combine 13x and -6x to get 7x.

$$x^{3}-5x^{2}+7x+13$$