Solve x^10y^5+x^4y^8

$$x ^ { 10 } y ^ { 5 } + x ^ { 4 } y ^ { 8 }$$

Factor

$$\left(x^{2}+y\right)x^{4}\left(x^{4}+y^{2}-yx^{2}\right)y^{5}$$

Solution Steps

Factor out x^{4}y^{5}.

$$x^{4}y^{5}\left(x^{6}+y^{3}\right)$$

Consider x^{6}+y^{3}. The sum of cubes can be factored using the rule: a^{3}+b^{3}=\left(a+b\right)\left(a^{2}-ab+b^{2}\right).

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

Rewrite the complete factored expression.

$$x^{4}y^{5}\left(x^{2}+y\right)\left(x^{4}+y^{2}-yx^{2}\right)$$

Evaluate

$$x^{4}y^{5}\left(x^{6}+y^{3}\right)$$