Solve 4(3-x)^2-(3-x)^3+3(3-x)

$$4 ( 3 - x ) ^ { 2 } - ( 3 - x ) ^ { 3 } + 3 ( 3 - x )$$

Evaluate

$$x^{3}-5x^{2}+18$$

Solution Steps

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

$$4\left(9-6x+x^{2}\right)-\left(3-x\right)^{3}+3\left(3-x\right)$$

Use the distributive property to multiply 4 by 9-6x+x^{2}.

$$36-24x+4x^{2}-\left(3-x\right)^{3}+3\left(3-x\right)$$

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

$$36-24x+4x^{2}-\left(27-27x+9x^{2}-x^{3}\right)+3\left(3-x\right)$$

To find the opposite of 27-27x+9x^{2}-x^{3}, find the opposite of each term.

$$36-24x+4x^{2}-27+27x-9x^{2}+x^{3}+3\left(3-x\right)$$

Subtract 27 from 36 to get 9.

$$9-24x+4x^{2}+27x-9x^{2}+x^{3}+3\left(3-x\right)$$

Combine -24x and 27x to get 3x.

$$9+3x+4x^{2}-9x^{2}+x^{3}+3\left(3-x\right)$$

Combine 4x^{2} and -9x^{2} to get -5x^{2}.

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

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

$$9+3x-5x^{2}+x^{3}+9-3x$$

Add 9 and 9 to get 18.

$$18+3x-5x^{2}+x^{3}-3x$$

Combine 3x and -3x to get 0.

$$18-5x^{2}+x^{3}$$

Expand

$$x^{3}-5x^{2}+18$$

Solution Steps

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

$$4\left(9-6x+x^{2}\right)-\left(3-x\right)^{3}+3\left(3-x\right)$$

Use the distributive property to multiply 4 by 9-6x+x^{2}.

$$36-24x+4x^{2}-\left(3-x\right)^{3}+3\left(3-x\right)$$

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

$$36-24x+4x^{2}-\left(27-27x+9x^{2}-x^{3}\right)+3\left(3-x\right)$$

To find the opposite of 27-27x+9x^{2}-x^{3}, find the opposite of each term.

$$36-24x+4x^{2}-27+27x-9x^{2}+x^{3}+3\left(3-x\right)$$

Subtract 27 from 36 to get 9.

$$9-24x+4x^{2}+27x-9x^{2}+x^{3}+3\left(3-x\right)$$

Combine -24x and 27x to get 3x.

$$9+3x+4x^{2}-9x^{2}+x^{3}+3\left(3-x\right)$$

Combine 4x^{2} and -9x^{2} to get -5x^{2}.

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

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

$$9+3x-5x^{2}+x^{3}+9-3x$$

Add 9 and 9 to get 18.

$$18+3x-5x^{2}+x^{3}-3x$$

Combine 3x and -3x to get 0.

$$18-5x^{2}+x^{3}$$