Solve (2x+3)(x-2)+(-x+4)(x+5)

$$( 2 x + 3 ) ( x - 2 ) + ( - x + 4 ) ( x + 5 )$$

Evaluate

$$x^{2}-2x+14$$

Solution Steps

Apply the distributive property by multiplying each term of 2x+3 by each term of x-2.

$$2x^{2}-4x+3x-6+\left(-x+4\right)\left(x+5\right)$$

Combine -4x and 3x to get -x.

$$2x^{2}-x-6+\left(-x+4\right)\left(x+5\right)$$

Apply the distributive property by multiplying each term of -x+4 by each term of x+5.

$$2x^{2}-x-6+\left(-x\right)x+5\left(-x\right)+4x+20$$

Combine -x and 4x to get 3x.

$$2x^{2}+3x-6+\left(-x\right)x+5\left(-x\right)+20$$

Add -6 and 20 to get 14.

$$2x^{2}+3x+14+\left(-x\right)x+5\left(-x\right)$$

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

$$2x^{2}+3x+14-x^{2}+5\left(-1\right)x$$

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

$$x^{2}+3x+14+5\left(-1\right)x$$

Multiply 5 and -1 to get -5.

$$x^{2}+3x+14-5x$$

Combine 3x and -5x to get -2x.

$$x^{2}-2x+14$$

Expand

$$x^{2}-2x+14$$

Solution Steps

Apply the distributive property by multiplying each term of 2x+3 by each term of x-2.

$$2x^{2}-4x+3x-6+\left(-x+4\right)\left(x+5\right)$$

Combine -4x and 3x to get -x.

$$2x^{2}-x-6+\left(-x+4\right)\left(x+5\right)$$

Apply the distributive property by multiplying each term of -x+4 by each term of x+5.

$$2x^{2}-x-6+\left(-x\right)x+5\left(-x\right)+4x+20$$

Combine -x and 4x to get 3x.

$$2x^{2}+3x-6+\left(-x\right)x+5\left(-x\right)+20$$

Add -6 and 20 to get 14.

$$2x^{2}+3x+14+\left(-x\right)x+5\left(-x\right)$$

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

$$2x^{2}+3x+14-x^{2}+5\left(-1\right)x$$

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

$$x^{2}+3x+14+5\left(-1\right)x$$

Multiply 5 and -1 to get -5.

$$x^{2}+3x+14-5x$$

Combine 3x and -5x to get -2x.

$$x^{2}-2x+14$$