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

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

Evaluate

$$\left(x-3\right)^{3}$$

Solution Steps

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

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

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

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

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

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

Use the distributive property to multiply -3 by 9-6x+x^{2}.

$$x^{3}-6x^{2}+9x-27+18x-3x^{2}$$

Combine 9x and 18x to get 27x.

$$x^{3}-6x^{2}+27x-27-3x^{2}$$

Combine -6x^{2} and -3x^{2} to get -9x^{2}.

$$x^{3}-9x^{2}+27x-27$$

Expand

$$x^{3}-9x^{2}+27x-27$$

Solution Steps

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

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

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

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

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

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

Use the distributive property to multiply -3 by 9-6x+x^{2}.

$$x^{3}-6x^{2}+9x-27+18x-3x^{2}$$

Combine 9x and 18x to get 27x.

$$x^{3}-6x^{2}+27x-27-3x^{2}$$

Combine -6x^{2} and -3x^{2} to get -9x^{2}.

$$x^{3}-9x^{2}+27x-27$$