Solve (-2x-5)(-x+1)+(-2x-5)(-x+4)

$$( - 2 x - 5 ) ( - x + 1 ) + ( - 2 x - 5 ) ( - x + 4 )$$

Evaluate

$$4x^{2}-25$$

Solution Steps

Apply the distributive property by multiplying each term of -2x-5 by each term of -x+1.

$$-2x\left(-x\right)-2x-5\left(-x\right)-5+\left(-2x-5\right)\left(-x+4\right)$$

Multiply -2 and -1 to get 2.

$$2xx-2x-5\left(-x\right)-5+\left(-2x-5\right)\left(-x+4\right)$$

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

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

Multiply -5 and -1 to get 5.

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

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

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

Apply the distributive property by multiplying each term of -2x-5 by each term of -x+4.

$$2x^{2}+3x-5-2x\left(-x\right)-8x-5\left(-x\right)-20$$

Multiply -2 and -1 to get 2.

$$2x^{2}+3x-5+2xx-8x-5\left(-x\right)-20$$

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

$$2x^{2}+3x-5+2x^{2}-8x-5\left(-x\right)-20$$

Multiply -5 and -1 to get 5.

$$2x^{2}+3x-5+2x^{2}-8x+5x-20$$

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

$$2x^{2}+3x-5+2x^{2}-3x-20$$

Combine 2x^{2} and 2x^{2} to get 4x^{2}.

$$4x^{2}+3x-5-3x-20$$

Combine 3x and -3x to get 0.

$$4x^{2}-5-20$$

Subtract 20 from -5 to get -25.

$$4x^{2}-25$$

Expand

$$4x^{2}-25$$

Solution Steps

Apply the distributive property by multiplying each term of -2x-5 by each term of -x+1.

$$-2x\left(-x\right)-2x-5\left(-x\right)-5+\left(-2x-5\right)\left(-x+4\right)$$

Multiply -2 and -1 to get 2.

$$2xx-2x-5\left(-x\right)-5+\left(-2x-5\right)\left(-x+4\right)$$

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

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

Multiply -5 and -1 to get 5.

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

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

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

Apply the distributive property by multiplying each term of -2x-5 by each term of -x+4.

$$2x^{2}+3x-5-2x\left(-x\right)-8x-5\left(-x\right)-20$$

Multiply -2 and -1 to get 2.

$$2x^{2}+3x-5+2xx-8x-5\left(-x\right)-20$$

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

$$2x^{2}+3x-5+2x^{2}-8x-5\left(-x\right)-20$$

Multiply -5 and -1 to get 5.

$$2x^{2}+3x-5+2x^{2}-8x+5x-20$$

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

$$2x^{2}+3x-5+2x^{2}-3x-20$$

Combine 2x^{2} and 2x^{2} to get 4x^{2}.

$$4x^{2}+3x-5-3x-20$$

Combine 3x and -3x to get 0.

$$4x^{2}-5-20$$

Subtract 20 from -5 to get -25.

$$4x^{2}-25$$