Question

Help with equation..

Answer 1

\[(5+\sqrt[3]{2})(25-5\sqrt[3]{2}+\sqrt[3]{4})\]

Answer 2

Those are cube roots.

Answer 3

You can either multiply everything out straight:\[(5+\sqrt[3]{2})(25-5\sqrt[3]{2}+\sqrt[3]{4})\]\[=5(25-5\sqrt[3]{2}+\sqrt[3]{4})+\sqrt[3]{2}(25-5\sqrt[3]{2}+\sqrt[3]{4})\]\[=75-25\sqrt[3]{2}+5\sqrt[3]{4}+25\sqrt[3]{2}-5\sqrt[3]{4}+\sqrt[3]{8}\]then just collect all the like terms (note the cube root of 8 is 2).

Answer 4

Or you can notice this is an application of:\[x^3+y^3=(x+y)(x^2-xy+y^2),x=5,y=\sqrt[3]{2}\]