Solve 2(x+1)(x-8)+9x^2-(x-2)^2=

$$2 ( x + 1 ) ( x - 8 ) + 9 x ^ { 2 } - ( x - 2 ) ^ { 2 } =$$

Evaluate

$$10\left(x-2\right)\left(x+1\right)$$

Solution Steps

Use the distributive property to multiply 2 by x+1.

$$\left(2x+2\right)\left(x-8\right)+9x^{2}-\left(x-2\right)^{2}$$

Use the distributive property to multiply 2x+2 by x-8 and combine like terms.

$$2x^{2}-14x-16+9x^{2}-\left(x-2\right)^{2}$$

Combine 2x^{2} and 9x^{2} to get 11x^{2}.

$$11x^{2}-14x-16-\left(x-2\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-2\right)^{2}.

$$11x^{2}-14x-16-\left(x^{2}-4x+4\right)$$

To find the opposite of x^{2}-4x+4, find the opposite of each term.

$$11x^{2}-14x-16-x^{2}+4x-4$$

Combine 11x^{2} and -x^{2} to get 10x^{2}.

$$10x^{2}-14x-16+4x-4$$

Combine -14x and 4x to get -10x.

$$10x^{2}-10x-16-4$$

Subtract 4 from -16 to get -20.

$$10x^{2}-10x-20$$

Expand

$$10x^{2}-10x-20$$

Solution Steps

Use the distributive property to multiply 2 by x+1.

$$\left(2x+2\right)\left(x-8\right)+9x^{2}-\left(x-2\right)^{2}$$

Use the distributive property to multiply 2x+2 by x-8 and combine like terms.

$$2x^{2}-14x-16+9x^{2}-\left(x-2\right)^{2}$$

Combine 2x^{2} and 9x^{2} to get 11x^{2}.

$$11x^{2}-14x-16-\left(x-2\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-2\right)^{2}.

$$11x^{2}-14x-16-\left(x^{2}-4x+4\right)$$

To find the opposite of x^{2}-4x+4, find the opposite of each term.

$$11x^{2}-14x-16-x^{2}+4x-4$$

Combine 11x^{2} and -x^{2} to get 10x^{2}.

$$10x^{2}-14x-16+4x-4$$

Combine -14x and 4x to get -10x.

$$10x^{2}-10x-16-4$$

Subtract 4 from -16 to get -20.

$$10x^{2}-10x-20$$