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

1 Answer
Apr 11, 2016

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.