Solve (-2x+1)(x^2-7x+5)-(-x^2-7x-8)(2x-1)

$$(-2x+1)( { x }^{ 2 } -7x+5)-(- { x }^{ 2 } -7x-8)(2x-1)$$

Evaluate

$$\left(2x-1\right)\left(14x+3\right)$$

Solution Steps

Use the distributive property to multiply -2x+1 by x^{2}-7x+5 and combine like terms.

$$-2x^{3}+15x^{2}-17x+5-\left(-x^{2}-7x-8\right)\left(2x-1\right)$$

Use the distributive property to multiply -x^{2}-7x-8 by 2x-1 and combine like terms.

$$-2x^{3}+15x^{2}-17x+5-\left(2\left(-x^{2}\right)x-\left(-x^{2}\right)-14x^{2}-9x+8\right)$$

Multiply -1 and -1 to get 1.

$$-2x^{3}+15x^{2}-17x+5-\left(2\left(-x^{2}\right)x+x^{2}-14x^{2}-9x+8\right)$$

Combine x^{2} and -14x^{2} to get -13x^{2}.

$$-2x^{3}+15x^{2}-17x+5-\left(2\left(-x^{2}\right)x-13x^{2}-9x+8\right)$$

To find the opposite of 2\left(-x^{2}\right)x-13x^{2}-9x+8, find the opposite of each term.

$$-2x^{3}+15x^{2}-17x+5-2\left(-x^{2}\right)x+13x^{2}+9x-8$$

Multiply -2 and -1 to get 2.

$$-2x^{3}+15x^{2}-17x+5+2x^{2}x+13x^{2}+9x-8$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$-2x^{3}+15x^{2}-17x+5+2x^{3}+13x^{2}+9x-8$$

Combine -2x^{3} and 2x^{3} to get 0.

$$15x^{2}-17x+5+13x^{2}+9x-8$$

Combine 15x^{2} and 13x^{2} to get 28x^{2}.

$$28x^{2}-17x+5+9x-8$$

Combine -17x and 9x to get -8x.

$$28x^{2}-8x+5-8$$

Subtract 8 from 5 to get -3.

$$28x^{2}-8x-3$$

Expand

$$28x^{2}-8x-3$$

Solution Steps

Use the distributive property to multiply -2x+1 by x^{2}-7x+5 and combine like terms.

$$-2x^{3}+15x^{2}-17x+5-\left(-x^{2}-7x-8\right)\left(2x-1\right)$$

Use the distributive property to multiply -x^{2}-7x-8 by 2x-1 and combine like terms.

$$-2x^{3}+15x^{2}-17x+5-\left(2\left(-x^{2}\right)x-\left(-x^{2}\right)-14x^{2}-9x+8\right)$$

Multiply -1 and -1 to get 1.

$$-2x^{3}+15x^{2}-17x+5-\left(2\left(-x^{2}\right)x+x^{2}-14x^{2}-9x+8\right)$$

Combine x^{2} and -14x^{2} to get -13x^{2}.

$$-2x^{3}+15x^{2}-17x+5-\left(2\left(-x^{2}\right)x-13x^{2}-9x+8\right)$$

To find the opposite of 2\left(-x^{2}\right)x-13x^{2}-9x+8, find the opposite of each term.

$$-2x^{3}+15x^{2}-17x+5-2\left(-x^{2}\right)x+13x^{2}+9x-8$$

Multiply -2 and -1 to get 2.

$$-2x^{3}+15x^{2}-17x+5+2x^{2}x+13x^{2}+9x-8$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$-2x^{3}+15x^{2}-17x+5+2x^{3}+13x^{2}+9x-8$$

Combine -2x^{3} and 2x^{3} to get 0.

$$15x^{2}-17x+5+13x^{2}+9x-8$$

Combine 15x^{2} and 13x^{2} to get 28x^{2}.

$$28x^{2}-17x+5+9x-8$$

Combine -17x and 9x to get -8x.

$$28x^{2}-8x+5-8$$

Subtract 8 from 5 to get -3.

$$28x^{2}-8x-3$$