Solve 2(x-3)^2-2(x-3)(x+3)-12(x+3)

$$2 ( x - 3 ) ^ { 2 } - 2 ( x - 3 ) ( x + 3 ) - 12 ( x + 3 )$$

Evaluate

$$-24x$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.

$$2\left(x^{2}-6x+9\right)-2\left(x-3\right)\left(x+3\right)-12\left(x+3\right)$$

Use the distributive property to multiply 2 by x^{2}-6x+9.

$$2x^{2}-12x+18-2\left(x-3\right)\left(x+3\right)-12\left(x+3\right)$$

Use the distributive property to multiply -12 by x+3.

$$2x^{2}-12x+18-2\left(x-3\right)\left(x+3\right)-12x-36$$

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

$$2x^{2}-12x+18+\left(-2x+6\right)\left(x+3\right)-12x-36$$

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

$$2x^{2}-12x+18-2x^{2}+18-12x-36$$

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

$$-12x+18+18-12x-36$$

Add 18 and 18 to get 36.

$$-12x+36-12x-36$$

Combine -12x and -12x to get -24x.

$$-24x+36-36$$

Subtract 36 from 36 to get 0.

$$-24x$$

Expand

$$-24x$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.

$$2\left(x^{2}-6x+9\right)-2\left(x-3\right)\left(x+3\right)-12\left(x+3\right)$$

Use the distributive property to multiply 2 by x^{2}-6x+9.

$$2x^{2}-12x+18-2\left(x-3\right)\left(x+3\right)-12\left(x+3\right)$$

Use the distributive property to multiply -12 by x+3.

$$2x^{2}-12x+18-2\left(x-3\right)\left(x+3\right)-12x-36$$

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

$$2x^{2}-12x+18+\left(-2x+6\right)\left(x+3\right)-12x-36$$

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

$$2x^{2}-12x+18-2x^{2}+18-12x-36$$

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

$$-12x+18+18-12x-36$$

Add 18 and 18 to get 36.

$$-12x+36-12x-36$$

Combine -12x and -12x to get -24x.

$$-24x+36-36$$

Subtract 36 from 36 to get 0.

$$-24x$$