Solve x(30-x)^2-4000

$$x ( 30 - x ) ^ { 2 } - 4000$$

Evaluate

$$\left(x-40\right)\left(x-10\right)^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(30-x\right)^{2}.

$$x\left(900-60x+x^{2}\right)-4000$$

Use the distributive property to multiply x by 900-60x+x^{2}.

$$900x-60x^{2}+x^{3}-4000$$

Expand

$$x^{3}-60x^{2}+900x-4000$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(30-x\right)^{2}.

$$x\left(900-60x+x^{2}\right)-4000$$

Use the distributive property to multiply x by 900-60x+x^{2}.

$$900x-60x^{2}+x^{3}-4000$$