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

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

Evaluate

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

Solution Steps

Multiply x+5 and x+5 to get \left(x+5\right)^{2}.

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

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

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

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

$$\left(x^{5}+15x^{4}+75x^{3}+125x^{2}\right)\left(x-5\right)$$

Use the distributive property to multiply x^{5}+15x^{4}+75x^{3}+125x^{2} by x-5 and combine like terms.

$$x^{6}+10x^{5}-250x^{3}-625x^{2}$$