Solve y=x^4(x-3)^3(x+1)^2

$$y = x ^ { 4 } ( x - 3 ) ^ { 3 } ( x + 1 ) ^ { 2 }$$

Solve for y

$$y=\left(x+1\right)^{2}\left(x-3\right)^{3}x^{4}$$

Solution Steps

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

$$y=x^{4}\left(x^{3}-9x^{2}+27x-27\right)\left(x+1\right)^{2}$$

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

$$y=x^{4}\left(x^{3}-9x^{2}+27x-27\right)\left(x^{2}+2x+1\right)$$

Use the distributive property to multiply x^{4} by x^{3}-9x^{2}+27x-27.

$$y=\left(x^{7}-9x^{6}+27x^{5}-27x^{4}\right)\left(x^{2}+2x+1\right)$$

Use the distributive property to multiply x^{7}-9x^{6}+27x^{5}-27x^{4} by x^{2}+2x+1 and combine like terms.

$$y=x^{9}-7x^{8}+10x^{7}+18x^{6}-27x^{5}-27x^{4}$$