Solve [x-(6+2i)][x-(6-2i)]

$$[ x - ( 6 + 2 i ) ] [ x - ( 6 - 2 i ) ]$$

Evaluate

$$\left(x+\left(-6-2i\right)\right)\left(x+\left(-6+2i\right)\right)$$

Solution Steps

Multiply -1 and 6+2i to get -6-2i.

$$\left(x+\left(-6-2i\right)\right)\left(x-\left(6-2i\right)\right)$$

Multiply -1 and 6-2i to get -6+2i.

$$\left(x+\left(-6-2i\right)\right)\left(x+\left(-6+2i\right)\right)$$

Apply the distributive property by multiplying each term of x+\left(-6-2i\right) by each term of x+\left(-6+2i\right).

$$x^{2}+\left(-6+2i\right)x+\left(-6-2i\right)x+40$$

Combine \left(-6+2i\right)x and \left(-6-2i\right)x to get -12x.

$$x^{2}-12x+40$$

Expand

$$x^{2}-12x+40$$

Solution Steps

Multiply -1 and 6+2i to get -6-2i.

$$\left(x+\left(-6-2i\right)\right)\left(x-\left(6-2i\right)\right)$$

Multiply -1 and 6-2i to get -6+2i.

$$\left(x+\left(-6-2i\right)\right)\left(x+\left(-6+2i\right)\right)$$

Apply the distributive property by multiplying each term of x+\left(-6-2i\right) by each term of x+\left(-6+2i\right).

$$x^{2}+\left(-6+2i\right)x+\left(-6-2i\right)x+40$$

Combine \left(-6+2i\right)x and \left(-6-2i\right)x to get -12x.

$$x^{2}-12x+40$$