Solve 2(x+3)(x-4)-(x-6)^2

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

Evaluate

$$x^{2}+10x-60$$

Solution Steps

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

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

Use the distributive property to multiply 2x+6 by x-4 and combine like terms.

$$2x^{2}-2x-24-\left(x-6\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-6\right)^{2}.

$$2x^{2}-2x-24-\left(x^{2}-12x+36\right)$$

To find the opposite of x^{2}-12x+36, find the opposite of each term.

$$2x^{2}-2x-24-x^{2}+12x-36$$

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

$$x^{2}-2x-24+12x-36$$

Combine -2x and 12x to get 10x.

$$x^{2}+10x-24-36$$

Subtract 36 from -24 to get -60.

$$x^{2}+10x-60$$

Expand

$$x^{2}+10x-60$$

Solution Steps

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

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

Use the distributive property to multiply 2x+6 by x-4 and combine like terms.

$$2x^{2}-2x-24-\left(x-6\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-6\right)^{2}.

$$2x^{2}-2x-24-\left(x^{2}-12x+36\right)$$

To find the opposite of x^{2}-12x+36, find the opposite of each term.

$$2x^{2}-2x-24-x^{2}+12x-36$$

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

$$x^{2}-2x-24+12x-36$$

Combine -2x and 12x to get 10x.

$$x^{2}+10x-24-36$$

Subtract 36 from -24 to get -60.

$$x^{2}+10x-60$$