Solve 36x^3(x-5)+24x^2(5-x)+60x(x-5)

$$36 { x }^{ 3 } (x-5)+24 { x }^{ 2 } (5-x)+60x(x-5)$$

Evaluate

$$12x\left(x-5\right)\left(3x^{2}-2x+5\right)$$

Solution Steps

Use the distributive property to multiply 36x^{3} by x-5.

$$36x^{4}-180x^{3}+24x^{2}\left(5-x\right)+60x\left(x-5\right)$$

Use the distributive property to multiply 24x^{2} by 5-x.

$$36x^{4}-180x^{3}+120x^{2}-24x^{3}+60x\left(x-5\right)$$

Combine -180x^{3} and -24x^{3} to get -204x^{3}.

$$36x^{4}-204x^{3}+120x^{2}+60x\left(x-5\right)$$

Use the distributive property to multiply 60x by x-5.

$$36x^{4}-204x^{3}+120x^{2}+60x^{2}-300x$$

Combine 120x^{2} and 60x^{2} to get 180x^{2}.

$$36x^{4}-204x^{3}+180x^{2}-300x$$

Expand

$$36x^{4}-204x^{3}+180x^{2}-300x$$

Solution Steps

Use the distributive property to multiply 36x^{3} by x-5.

$$36x^{4}-180x^{3}+24x^{2}\left(5-x\right)+60x\left(x-5\right)$$

Use the distributive property to multiply 24x^{2} by 5-x.

$$36x^{4}-180x^{3}+120x^{2}-24x^{3}+60x\left(x-5\right)$$

Combine -180x^{3} and -24x^{3} to get -204x^{3}.

$$36x^{4}-204x^{3}+120x^{2}+60x\left(x-5\right)$$

Use the distributive property to multiply 60x by x-5.

$$36x^{4}-204x^{3}+120x^{2}+60x^{2}-300x$$

Combine 120x^{2} and 60x^{2} to get 180x^{2}.

$$36x^{4}-204x^{3}+180x^{2}-300x$$