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

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

Evaluate

$$\left(7-2x\right)\left(5-x\right)^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(5-x\right)^{3}.

$$2\left(125-75x+15x^{2}-x^{3}\right)-3\left(5-x\right)^{2}$$

Use the distributive property to multiply 2 by 125-75x+15x^{2}-x^{3}.

$$250-150x+30x^{2}-2x^{3}-3\left(5-x\right)^{2}$$

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

$$250-150x+30x^{2}-2x^{3}-3\left(25-10x+x^{2}\right)$$

Use the distributive property to multiply -3 by 25-10x+x^{2}.

$$250-150x+30x^{2}-2x^{3}-75+30x-3x^{2}$$

Subtract 75 from 250 to get 175.

$$175-150x+30x^{2}-2x^{3}+30x-3x^{2}$$

Combine -150x and 30x to get -120x.

$$175-120x+30x^{2}-2x^{3}-3x^{2}$$

Combine 30x^{2} and -3x^{2} to get 27x^{2}.

$$175-120x+27x^{2}-2x^{3}$$

Expand

$$175-120x+27x^{2}-2x^{3}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(5-x\right)^{3}.

$$2\left(125-75x+15x^{2}-x^{3}\right)-3\left(5-x\right)^{2}$$

Use the distributive property to multiply 2 by 125-75x+15x^{2}-x^{3}.

$$250-150x+30x^{2}-2x^{3}-3\left(5-x\right)^{2}$$

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

$$250-150x+30x^{2}-2x^{3}-3\left(25-10x+x^{2}\right)$$

Use the distributive property to multiply -3 by 25-10x+x^{2}.

$$250-150x+30x^{2}-2x^{3}-75+30x-3x^{2}$$

Subtract 75 from 250 to get 175.

$$175-150x+30x^{2}-2x^{3}+30x-3x^{2}$$

Combine -150x and 30x to get -120x.

$$175-120x+30x^{2}-2x^{3}-3x^{2}$$

Combine 30x^{2} and -3x^{2} to get 27x^{2}.

$$175-120x+27x^{2}-2x^{3}$$