Solve f(x)=x^2(1-x)^3

$$f ( x ) = x ^ { 2 } ( 1 - x ) ^ { 3 }$$

Evaluate

$$x^{2}\left(1-x\right)^{3}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(1-x\right)^{3}.

$$x^{2}\left(1-3x+3x^{2}-x^{3}\right)$$

Use the distributive property to multiply x^{2} by 1-3x+3x^{2}-x^{3}.

$$x^{2}-3x^{3}+3x^{4}-x^{5}$$

Expand

$$x^{2}-3x^{3}+3x^{4}-x^{5}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(1-x\right)^{3}.

$$x^{2}\left(1-3x+3x^{2}-x^{3}\right)$$

Use the distributive property to multiply x^{2} by 1-3x+3x^{2}-x^{3}.

$$x^{2}-3x^{3}+3x^{4}-x^{5}$$