Solve 2(x-3)(x+3)-(x-4)^2

$$2 ( x - 3 ) ( x + 3 ) - ( x - 4 ) ^ { 2 }$$

Evaluate

$$x^{2}+8x-34$$

Solution Steps

Use the distributive property to multiply 2 by x-3.

$$\left(2x-6\right)\left(x+3\right)-\left(x-4\right)^{2}$$

Use the distributive property to multiply 2x-6 by x+3 and combine like terms.

$$2x^{2}-18-\left(x-4\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-4\right)^{2}.

$$2x^{2}-18-\left(x^{2}-8x+16\right)$$

To find the opposite of x^{2}-8x+16, find the opposite of each term.

$$2x^{2}-18-x^{2}+8x-16$$

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

$$x^{2}-18+8x-16$$

Subtract 16 from -18 to get -34.

$$x^{2}-34+8x$$

Expand

$$x^{2}+8x-34$$

Solution Steps

Use the distributive property to multiply 2 by x-3.

$$\left(2x-6\right)\left(x+3\right)-\left(x-4\right)^{2}$$

Use the distributive property to multiply 2x-6 by x+3 and combine like terms.

$$2x^{2}-18-\left(x-4\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-4\right)^{2}.

$$2x^{2}-18-\left(x^{2}-8x+16\right)$$

To find the opposite of x^{2}-8x+16, find the opposite of each term.

$$2x^{2}-18-x^{2}+8x-16$$

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

$$x^{2}-18+8x-16$$

Subtract 16 from -18 to get -34.

$$x^{2}-34+8x$$