Question

Can someone help in solving polynomials function .. how to factor X^6 x Y^3+Y^9

Answer 1

\[X ^{6}\times Y ^{3}+Y ^{9}\]

Answer 2

Bring out the \(Y^3\) term since it is common to both addends, then factor the resulting cubic (see - http://en.wikipedia.org/wiki/Factorization#Sum.2Fdifference_of_two_cubes)
$$
\large{
Y^3\left (X^6+Y^6\right )\\
=Y^3\left (X^{\left (2\right)^{3} }+Y^{\left (2\right)^{3} }\right ) \\
Y^3(X^2 + Y^2)\left (X^{\left (2\right)^{2}}-X^{\left (2\right)}Y^{\left (2\right)}+Y^{\left (2\right)^{2}}\right )\\
}
$$
Which I'll leave for you to simplify.