Solve (x-8)(x-(3+i)(x-(3-i)

$$( x - 8 ) ( x - ( 3 + i ) ( x - ( 3 - i )$$

Evaluate

$$\left(x-8\right)\left(\left(-2-i\right)x+10\right)$$

Solution Steps

Use the distributive property to multiply x-8 by x-\left(3+i\right)\left(x-\left(3-i\right)\right).

$$x\left(x-\left(3+i\right)\left(x-\left(3-i\right)\right)\right)-8\left(x-\left(3+i\right)\left(x-\left(3-i\right)\right)\right)$$

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

$$x\left(x+\left(-3-i\right)\left(x-\left(3-i\right)\right)\right)-8\left(x-\left(3+i\right)\left(x-\left(3-i\right)\right)\right)$$

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

$$x\left(x+\left(-3-i\right)\left(x+\left(-3+i\right)\right)\right)-8\left(x-\left(3+i\right)\left(x-\left(3-i\right)\right)\right)$$

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

$$x\left(x+\left(-3-i\right)x+10\right)-8\left(x-\left(3+i\right)\left(x-\left(3-i\right)\right)\right)$$

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

$$x\left(\left(-2-i\right)x+10\right)-8\left(x-\left(3+i\right)\left(x-\left(3-i\right)\right)\right)$$

Use the distributive property to multiply x by \left(-2-i\right)x+10.

$$\left(-2-i\right)x^{2}+10x-8\left(x-\left(3+i\right)\left(x-\left(3-i\right)\right)\right)$$

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

$$\left(-2-i\right)x^{2}+10x-8\left(x+\left(-3-i\right)\left(x-\left(3-i\right)\right)\right)$$

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

$$\left(-2-i\right)x^{2}+10x-8\left(x+\left(-3-i\right)\left(x+\left(-3+i\right)\right)\right)$$

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

$$\left(-2-i\right)x^{2}+10x-8\left(x+\left(-3-i\right)x+10\right)$$

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

$$\left(-2-i\right)x^{2}+10x-8\left(\left(-2-i\right)x+10\right)$$

Use the distributive property to multiply -8 by \left(-2-i\right)x+10.

$$\left(-2-i\right)x^{2}+10x+\left(16+8i\right)x-80$$

Combine 10x and \left(16+8i\right)x to get \left(26+8i\right)x.

$$\left(-2-i\right)x^{2}+\left(26+8i\right)x-80$$

Expand

$$\left(-2-i\right)x^{2}+\left(26+8i\right)x-80$$

Solution Steps

Use the distributive property to multiply x-8 by x-\left(3+i\right)\left(x-\left(3-i\right)\right).

$$x\left(x-\left(3+i\right)\left(x-\left(3-i\right)\right)\right)-8\left(x-\left(3+i\right)\left(x-\left(3-i\right)\right)\right)$$

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

$$x\left(x+\left(-3-i\right)\left(x-\left(3-i\right)\right)\right)-8\left(x-\left(3+i\right)\left(x-\left(3-i\right)\right)\right)$$

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

$$x\left(x+\left(-3-i\right)\left(x+\left(-3+i\right)\right)\right)-8\left(x-\left(3+i\right)\left(x-\left(3-i\right)\right)\right)$$

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

$$x\left(x+\left(-3-i\right)x+10\right)-8\left(x-\left(3+i\right)\left(x-\left(3-i\right)\right)\right)$$

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

$$x\left(\left(-2-i\right)x+10\right)-8\left(x-\left(3+i\right)\left(x-\left(3-i\right)\right)\right)$$

Use the distributive property to multiply x by \left(-2-i\right)x+10.

$$\left(-2-i\right)x^{2}+10x-8\left(x-\left(3+i\right)\left(x-\left(3-i\right)\right)\right)$$

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

$$\left(-2-i\right)x^{2}+10x-8\left(x+\left(-3-i\right)\left(x-\left(3-i\right)\right)\right)$$

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

$$\left(-2-i\right)x^{2}+10x-8\left(x+\left(-3-i\right)\left(x+\left(-3+i\right)\right)\right)$$

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

$$\left(-2-i\right)x^{2}+10x-8\left(x+\left(-3-i\right)x+10\right)$$

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

$$\left(-2-i\right)x^{2}+10x-8\left(\left(-2-i\right)x+10\right)$$

Use the distributive property to multiply -8 by \left(-2-i\right)x+10.

$$\left(-2-i\right)x^{2}+10x+\left(16+8i\right)x-80$$

Combine 10x and \left(16+8i\right)x to get \left(26+8i\right)x.

$$\left(-2-i\right)x^{2}+\left(26+8i\right)x-80$$