Suppose we want to factorise,

2x + 4

Find, we find common factors individually

2x = 2 × x

4 = 2 × 2

Since 2 is common, we take that out

So,

2x + 4 = 2 × x + 2 × 2

= 2 (x + 2)

So,

2x + 4 = 2 × (x + 2)

Let’s take another example

##
**
2
**
**
x
**
**
y + 2y
**

Finding factors

2xy = 2 × x × y

2y = 2 × y

So, 2 & y are the common factors.

So,

2xy + 2y = 2 × x × y + 2 × y

= 2 × y (x + 1)

= 2y (x + 1)

So,

2xy + 2y = 2y (x + 1)

###
5x
^{
2
}
y + 10x

Finding factors

5x
^{
2
}
y = 5 × x
^{
2
}
× y

= 5 × x × x × y

10x = 10 × x

= 2 × 5 × x

So,

5x
^{
2
}
y + 10x = 5 × x × x × y + 2 × 5 × x

= 5 × x (x × y + 2)

= 5x (xy + 2)