# Math Help - Factorising algebraic expression

1. ## Factorising algebraic expression

What method do I use to factorise $16x^4y + 2xy$?

The answer is $2xy(2x+1)(4x^2-2x+1)$

Thanks

2. One way to do it is to first take out the common factor of $2xy$:

$2xy(8x^3+1)$

You can then see (or test) values of $x$ that will make $8x^3+1=0$

In this case:

$P\left (-\frac{1}{2}\right )=0$

$\therefore (2x+1)$ is a factor.

Then if you divide $8x^3+1$ by $2x+1$ you'll get the quadratic factor.

3. $=2xy(8x^3+1)=2xy[(2x)^3+1]$
$=2xy(2x+1)(4x^2-2x+1)$

4. Lovemath is using the fact that $x^3+ y^3)= (x+ y)(x^2- xy+ y^2)$.

It is useful to know that, for all n, $x^n- y^n= (x- y)(x^{n-1}+ x^{n-2}y+$ $\cdot\cdot\cdot+ xy^{n-2}+ y^{n-1})$

and, for all odd n, $x^n+ y^n= (x+ y)(x^{n-1}- x^{n-1}y+ \cdot\cdot\cdot- xy^{n-1}+ y^n)$.