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

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

Evaluate

$$9-2x^{2}$$

Solution Steps

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

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

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

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

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

$$2x^{2}-12x+18-\left(4x^{2}-12x+9\right)$$

To find the opposite of 4x^{2}-12x+9, find the opposite of each term.

$$2x^{2}-12x+18-4x^{2}+12x-9$$

Combine 2x^{2} and -4x^{2} to get -2x^{2}.

$$-2x^{2}-12x+18+12x-9$$

Combine -12x and 12x to get 0.

$$-2x^{2}+18-9$$

Subtract 9 from 18 to get 9.

$$-2x^{2}+9$$

Expand

$$9-2x^{2}$$

Solution Steps

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

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

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

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

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

$$2x^{2}-12x+18-\left(4x^{2}-12x+9\right)$$

To find the opposite of 4x^{2}-12x+9, find the opposite of each term.

$$2x^{2}-12x+18-4x^{2}+12x-9$$

Combine 2x^{2} and -4x^{2} to get -2x^{2}.

$$-2x^{2}-12x+18+12x-9$$

Combine -12x and 12x to get 0.

$$-2x^{2}+18-9$$

Subtract 9 from 18 to get 9.

$$-2x^{2}+9$$