# How do you factor 36x^2y^6 - 16?

Mar 10, 2018

$4 \cdot \left(3 x {y}^{3} + 2\right) \cdot \left(3 x {y}^{3} - 2\right)$

#### Explanation:

$36 {x}^{2} {y}^{6} - 16$

= ((2^2+3^2*x^2) * y^6) - 16)

Because $\left({a}^{2} - {b}^{2}\right)$ can be factored into $\left(a + b\right) \cdot \left(a - b\right)$

From the simplified expression above, we can factorise the numbers as it is.

Simply half the index numbers as you would normally when you square root a number with an index.

Therefore:
$\left(\left[\left(3 x {y}^{3} + 2\right) \cdot \left(3 x {y}^{3} - 2\right)\right] - 16\right)$

We can also square root the 16

So
$4 \cdot \left(3 x {y}^{3} + 2\right) \cdot \left(3 x {y}^{3} - 2\right)$