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

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

Evaluate

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

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}.

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

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

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

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

$$250-150x+30x^{2}-2x^{3}-3\left(125-75x+15x^{2}-x^{3}\right)$$

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

$$250-150x+30x^{2}-2x^{3}-375+225x-45x^{2}+3x^{3}$$

Subtract 375 from 250 to get -125.

$$-125-150x+30x^{2}-2x^{3}+225x-45x^{2}+3x^{3}$$

Combine -150x and 225x to get 75x.

$$-125+75x+30x^{2}-2x^{3}-45x^{2}+3x^{3}$$

Combine 30x^{2} and -45x^{2} to get -15x^{2}.

$$-125+75x-15x^{2}-2x^{3}+3x^{3}$$

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

$$-125+75x-15x^{2}+x^{3}$$

Expand

$$x^{3}-15x^{2}+75x-125$$

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}.

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

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

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

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

$$250-150x+30x^{2}-2x^{3}-3\left(125-75x+15x^{2}-x^{3}\right)$$

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

$$250-150x+30x^{2}-2x^{3}-375+225x-45x^{2}+3x^{3}$$

Subtract 375 from 250 to get -125.

$$-125-150x+30x^{2}-2x^{3}+225x-45x^{2}+3x^{3}$$

Combine -150x and 225x to get 75x.

$$-125+75x+30x^{2}-2x^{3}-45x^{2}+3x^{3}$$

Combine 30x^{2} and -45x^{2} to get -15x^{2}.

$$-125+75x-15x^{2}-2x^{3}+3x^{3}$$

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

$$-125+75x-15x^{2}+x^{3}$$