Solve x(3x-6)^2-(x-5)^2

$$x ( 3 x - 6 ) ^ { 2 } - ( x - 5 ) ^ { 2 }$$

Evaluate

$$9x\left(x-2\right)^{2}-\left(x-5\right)^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-6\right)^{2}.

$$x\left(9x^{2}-36x+36\right)-\left(x-5\right)^{2}$$

Use the distributive property to multiply x by 9x^{2}-36x+36.

$$9x^{3}-36x^{2}+36x-\left(x-5\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-5\right)^{2}.

$$9x^{3}-36x^{2}+36x-\left(x^{2}-10x+25\right)$$

To find the opposite of x^{2}-10x+25, find the opposite of each term.

$$9x^{3}-36x^{2}+36x-x^{2}+10x-25$$

Combine -36x^{2} and -x^{2} to get -37x^{2}.

$$9x^{3}-37x^{2}+36x+10x-25$$

Combine 36x and 10x to get 46x.

$$9x^{3}-37x^{2}+46x-25$$

Expand

$$9x^{3}-37x^{2}+46x-25$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-6\right)^{2}.

$$x\left(9x^{2}-36x+36\right)-\left(x-5\right)^{2}$$

Use the distributive property to multiply x by 9x^{2}-36x+36.

$$9x^{3}-36x^{2}+36x-\left(x-5\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-5\right)^{2}.

$$9x^{3}-36x^{2}+36x-\left(x^{2}-10x+25\right)$$

To find the opposite of x^{2}-10x+25, find the opposite of each term.

$$9x^{3}-36x^{2}+36x-x^{2}+10x-25$$

Combine -36x^{2} and -x^{2} to get -37x^{2}.

$$9x^{3}-37x^{2}+36x+10x-25$$

Combine 36x and 10x to get 46x.

$$9x^{3}-37x^{2}+46x-25$$