Question

How do you factor the expression `49x^6 + 126x^3y^2 + 81y^4`?

Answer 1

`49x^6+126x^3y^2+81y^4 = (7x^3+9y^2)^2`

Explanation:

This is a perfect square trinomial of the form:

`a^2+2ab+b^2 = (a+b)^2`

with `a=7x^3` and `b=9y^2`

`49x^6+126x^3y^2+81y^4`

`= (7x^3)^2+2(7x^3)(9y^2)+(9y)^2`

`= (7x^3+9y^2)^2`

No further factorisation is possible since the remaining terms in `x` and `y` are of distinct prime degrees.