# How do you factor by grouping. 4+5xy-10y-2x?

Mar 12, 2018

$\left(2 - x\right) \left(2 - 5 y\right)$

#### Explanation:

If you have four terms without a common factor you need to group them.

Grouping like this $\left(4 + 5 x y\right) + \left(- 10 y - 2 x\right)$ achieves little.

Group the terms differently:

$\left(4 - 2 x\right) + \left(5 x y - 10 y\right) \text{ } \leftarrow$ find the HCF of each bracket

$= 2 \left(2 - x\right) \textcolor{b l u e}{+ 5 y \left(x - 2\right)} \text{ } \leftarrow$ divide $- 1$ out as a factor

$= 2 \left(2 - x\right) - 5 y \left(- x + 2\right) \text{ } \leftarrow$ the signs change

$2 \left(2 - x\right) - 5 y \left(2 - x\right) \text{ } \leftarrow$ makes equal brackets

$\left(2 - x\right) \left(2 - 5 y\right) \text{ } \leftarrow$ there are two factor

OR:

$\left(4 - 10 y\right) + \left(- 2 x + 5 x y\right)$

$= 2 \left(2 - 5 y\right) + x \left(- 2 + 5 y\right)$

$= 2 \left(2 - 5 y\right) - x \left(2 - 5 y\right)$

$= \left(2 - 5 y\right) \left(2 - x\right)$