Question

How do you factor 2x^3+5y^3

Answer 1

All you do is...

`\mathrm{Apply\:sum\:of\:cubes\:rule:\:}x^3+y^3=\left(x+y\right)\left(x^2-xy+y^2\right)`


`2x^3+5y^3=\left(\sqrt[3]{2}x+\sqrt[3]{5}y\right)\left(\left(\sqrt[3]{2}\right)^2x^2-\sqrt[3]{2}\sqrt[3]{5}xy+\left(\sqrt[3]{5}\right)^2y^2\right)`

`\left(\sqrt[3]{2}x+\sqrt[3]{5}y\right)\left(\left(\sqrt[3]{2}\right)^2x^2-\sqrt[3]{2}\sqrt[3]{5}xy+\left(\sqrt[3]{5}\right)^2y^2\right) \ \textgreater \ Refine`


`\left(\sqrt[3]{2}x+\sqrt[3]{5}y\right)\left(2^{(2)/(3)}x^2-\sqrt[3]{10}xy+5^{(2)/(3)}y^2\right)`

Hope this helps!