Solve 3x^2y^3-24x^2

$$3 x ^ { 2 } y ^ { 3 } - 24 x ^ { 2 }$$

Factor

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

Solution Steps

Factor out 3.

$$3\left(x^{2}y^{3}-8x^{2}\right)$$

Consider x^{2}y^{3}-8x^{2}. Factor out x^{2}.

$$x^{2}\left(y^{3}-8\right)$$

Consider y^{3}-8. Rewrite y^{3}-8 as y^{3}-2^{3}. The difference of cubes can be factored using the rule: a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right).

$$\left(y-2\right)\left(y^{2}+2y+4\right)$$

Rewrite the complete factored expression. Polynomial y^{2}+2y+4 is not factored since it does not have any rational roots.

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

Evaluate

$$3x^{2}\left(y^{3}-8\right)$$