Factorise 5x + 15
Find the highest common factor of 5 and 15
5
There is no x in the second term, so no highest common factor in x needed
Write each term as 5 × "something"
5 × x + 5 × 3
"Take out" the 5
5(x + 3)
5(x + 3)
Write each term as 6x × "something"
6x × 5x - 6x × 4
"Take out" the 6x
6x(5x - 4)
6x(5x - 4)
Factorise ab + 3b + 2a + 6
Method 1
Notice that ab and 3b have a common factor of b
Notice that 2a and 6 have a common factor of 2
Factorise the first two terms, using b as a common factor
b(a + 3) + 2a + 6
Factorise the second two terms, using 2 as a common factor
b(a + 3) + 2(a + 3)
(a + 3) is a common bracket
We can factorise using (a + 3) as a factor
(a + 3)(b + 2)
Method 2
Notice that ab and 2a have a common factor of a
Notice that 3b and 6 have a common factor of 3
Rewrite the expression grouping these terms together
ab + 2a + 3b + 6
Factorise the first two terms, using a as a common factor
a(b + 2) + 3b + 6
Factorise the second two terms, using 3 as a common factor
a(b + 2) + 3(b + 2)
(b + 2) is a common bracket
We can factorise using (b + 2) as a factor
(b + 2)(a + 3)