Question

Factorise the following:

36 – (a + 2b)² 

Answer 1

To factorise 36 – (a + 2b)², we can treat this as a difference of squares.

We have:

36 – (a + 2b)² 

Notice that 36 = 6², so the expression is of the form A² – B², where:

A = 6 and B = a + 2b

Now, apply the difference of squares formula:

A² – B² = (A – B) (A + B)

Substitute A and B into the formula:

(6 – (a + 2b))(6 + (a + 2b))

Now simplify:

(6 – a – 2b) (6 + a + 2b)

Thus, the factorised form of 36 – (a + 2b)² is (6 – a – 2b) (6 + a + 2b).