Solve f(x)=x^2(x-3)(x+5)^2

$$f ( x ) = x ^ { 2 } ( x - 3 ) ( x + 5 ) ^ { 2 }$$

Evaluate

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

Solution Steps

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

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

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

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

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

$$x^{5}+7x^{4}-5x^{3}-75x^{2}$$

Expand

$$x^{5}+7x^{4}-5x^{3}-75x^{2}$$

Solution Steps

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

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

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

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

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

$$x^{5}+7x^{4}-5x^{3}-75x^{2}$$