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

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

Solve for y

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

Solution Steps

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

$$y=\left(x+3\right)x^{3}\left(x+1\right)\left(x^{3}-6x^{2}+12x-8\right)$$

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

$$y=\left(x^{4}+3x^{3}\right)\left(x+1\right)\left(x^{3}-6x^{2}+12x-8\right)$$

Use the distributive property to multiply x^{4}+3x^{3} by x+1 and combine like terms.

$$y=\left(x^{5}+4x^{4}+3x^{3}\right)\left(x^{3}-6x^{2}+12x-8\right)$$

Use the distributive property to multiply x^{5}+4x^{4}+3x^{3} by x^{3}-6x^{2}+12x-8 and combine like terms.

$$y=x^{8}-2x^{7}-9x^{6}+22x^{5}+4x^{4}-24x^{3}$$