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

$$( 2 x - 1 ) \cdot ( x + 2 ) + ( 3 + x ) \cdot ( - 5 - x ) =$$

Evaluate

$$x^{2}-5x-17$$

Solution Steps

Apply the distributive property by multiplying each term of 2x-1 by each term of x+2.

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

Combine 4x and -x to get 3x.

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

Apply the distributive property by multiplying each term of 3+x by each term of -5-x.

$$2x^{2}+3x-2-15-3x-5x-x^{2}$$

Combine -3x and -5x to get -8x.

$$2x^{2}+3x-2-15-8x-x^{2}$$

Subtract 15 from -2 to get -17.

$$2x^{2}+3x-17-8x-x^{2}$$

Combine 3x and -8x to get -5x.

$$2x^{2}-5x-17-x^{2}$$

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

$$x^{2}-5x-17$$

Expand

$$x^{2}-5x-17$$

Solution Steps

Apply the distributive property by multiplying each term of 2x-1 by each term of x+2.

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

Combine 4x and -x to get 3x.

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

Apply the distributive property by multiplying each term of 3+x by each term of -5-x.

$$2x^{2}+3x-2-15-3x-5x-x^{2}$$

Combine -3x and -5x to get -8x.

$$2x^{2}+3x-2-15-8x-x^{2}$$

Subtract 15 from -2 to get -17.

$$2x^{2}+3x-17-8x-x^{2}$$

Combine 3x and -8x to get -5x.

$$2x^{2}-5x-17-x^{2}$$

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

$$x^{2}-5x-17$$