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

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

Evaluate

$$3\left(x+5\right)$$

Solution Steps

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

$$2x^{2}+x-2x-1-2\left(x-4\right)\left(x+2\right)$$

Combine x and -2x to get -x.

$$2x^{2}-x-1-2\left(x-4\right)\left(x+2\right)$$

Use the distributive property to multiply -2 by x-4.

$$2x^{2}-x-1+\left(-2x+8\right)\left(x+2\right)$$

Apply the distributive property by multiplying each term of -2x+8 by each term of x+2.

$$2x^{2}-x-1-2x^{2}-4x+8x+16$$

Combine -4x and 8x to get 4x.

$$2x^{2}-x-1-2x^{2}+4x+16$$

Combine 2x^{2} and -2x^{2} to get 0.

$$-x-1+4x+16$$

Combine -x and 4x to get 3x.

$$3x-1+16$$

Add -1 and 16 to get 15.

$$3x+15$$

Expand

$$3x+15$$

Solution Steps

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

$$2x^{2}+x-2x-1-2\left(x-4\right)\left(x+2\right)$$

Combine x and -2x to get -x.

$$2x^{2}-x-1-2\left(x-4\right)\left(x+2\right)$$

Use the distributive property to multiply -2 by x-4.

$$2x^{2}-x-1+\left(-2x+8\right)\left(x+2\right)$$

Apply the distributive property by multiplying each term of -2x+8 by each term of x+2.

$$2x^{2}-x-1-2x^{2}-4x+8x+16$$

Combine -4x and 8x to get 4x.

$$2x^{2}-x-1-2x^{2}+4x+16$$

Combine 2x^{2} and -2x^{2} to get 0.

$$-x-1+4x+16$$

Combine -x and 4x to get 3x.

$$3x-1+16$$

Add -1 and 16 to get 15.

$$3x+15$$