Solve 2(x-3)^2-3(x+1)^2

$$2 ( x - 3 ) ^ { 2 } - 3 ( x + 1 ) ^ { 2 }$$

Evaluate

$$15-18x-x^{2}$$

Solution Steps

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

$$2\left(x^{2}-6x+9\right)-3\left(x+1\right)^{2}$$

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

$$2x^{2}-12x+18-3\left(x+1\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.

$$2x^{2}-12x+18-3\left(x^{2}+2x+1\right)$$

Use the distributive property to multiply -3 by x^{2}+2x+1.

$$2x^{2}-12x+18-3x^{2}-6x-3$$

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

$$-x^{2}-12x+18-6x-3$$

Combine -12x and -6x to get -18x.

$$-x^{2}-18x+18-3$$

Subtract 3 from 18 to get 15.

$$-x^{2}-18x+15$$

Expand

$$15-18x-x^{2}$$

Solution Steps

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

$$2\left(x^{2}-6x+9\right)-3\left(x+1\right)^{2}$$

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

$$2x^{2}-12x+18-3\left(x+1\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.

$$2x^{2}-12x+18-3\left(x^{2}+2x+1\right)$$

Use the distributive property to multiply -3 by x^{2}+2x+1.

$$2x^{2}-12x+18-3x^{2}-6x-3$$

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

$$-x^{2}-12x+18-6x-3$$

Combine -12x and -6x to get -18x.

$$-x^{2}-18x+18-3$$

Subtract 3 from 18 to get 15.

$$-x^{2}-18x+15$$