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

1 Answer
Apr 11, 2016

Answer:

#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.