Question

Factorise the following:

3a² – 6a – ka + 2k + am – 2m

Answer 1

Step 1: Group the terms

Group them in convenient pairs:

(3a² – 6a) + (–ka + am)  + (2k – 2m)

Step 2: Factor each group

1. From 3a² – 6a, factor out 3a:

3a(a – 2)

2. From –ka + am, factor out a:

a(–k + m) = a(m – k)

3. From 2k – 2m, factor out 2:

2(k – m) = –2(m – k)

Step 3: Rewrite the expression using the common factor (a – 2) or (m – k)

Now we have:

3a(a – 2) + a(m – k) – 2(m – k)

Group the terms with (m – k):

a(m – k) – 2(m – k) = (m – k) (a – 2)

Step 4: Factor out the common binomial (a – 2)

(a – 2) (3a + m – k)