Solve (-x+3)(3x-1)+(x+5)(2x-2)

$$(-x+3)(3x-1)+(x+5)(2x-2)$$

Evaluate

$$-x^{2}+18x-13$$

Solution Steps

Apply the distributive property by multiplying each term of -x+3 by each term of 3x-1.

$$3\left(-x\right)x-\left(-x\right)+9x-3+\left(x+5\right)\left(2x-2\right)$$

Multiply -1 and -1 to get 1.

$$3\left(-x\right)x+x+9x-3+\left(x+5\right)\left(2x-2\right)$$

Combine x and 9x to get 10x.

$$3\left(-x\right)x+10x-3+\left(x+5\right)\left(2x-2\right)$$

Apply the distributive property by multiplying each term of x+5 by each term of 2x-2.

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

Combine -2x and 10x to get 8x.

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

Combine 10x and 8x to get 18x.

$$3\left(-x\right)x+18x-3+2x^{2}-10$$

Subtract 10 from -3 to get -13.

$$3\left(-x\right)x+18x-13+2x^{2}$$

Multiply 3 and -1 to get -3.

$$-3xx+18x-13+2x^{2}$$

Multiply x and x to get x^{2}.

$$-3x^{2}+18x-13+2x^{2}$$

Combine -3x^{2} and 2x^{2} to get -x^{2}.

$$-x^{2}+18x-13$$

Expand

$$-x^{2}+18x-13$$

Solution Steps

Apply the distributive property by multiplying each term of -x+3 by each term of 3x-1.

$$3\left(-x\right)x-\left(-x\right)+9x-3+\left(x+5\right)\left(2x-2\right)$$

Multiply -1 and -1 to get 1.

$$3\left(-x\right)x+x+9x-3+\left(x+5\right)\left(2x-2\right)$$

Combine x and 9x to get 10x.

$$3\left(-x\right)x+10x-3+\left(x+5\right)\left(2x-2\right)$$

Apply the distributive property by multiplying each term of x+5 by each term of 2x-2.

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

Combine -2x and 10x to get 8x.

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

Combine 10x and 8x to get 18x.

$$3\left(-x\right)x+18x-3+2x^{2}-10$$

Subtract 10 from -3 to get -13.

$$3\left(-x\right)x+18x-13+2x^{2}$$

Multiply 3 and -1 to get -3.

$$-3xx+18x-13+2x^{2}$$

Multiply x and x to get x^{2}.

$$-3x^{2}+18x-13+2x^{2}$$

Combine -3x^{2} and 2x^{2} to get -x^{2}.

$$-x^{2}+18x-13$$