Question

Factorise:

27a²b – 75b³

Answer 1

We are given the expression:

27a²b – 75b³

Step 1: Factor out the common factor:

The common factor in both terms is b, so we can factor out b:

27a²b – 75b³ = b(27a² – 75b²)

Step 2: Factor further:

Now, we can factor 27a² – 75b².

Notice that both terms have a common factor of 3:

27a² – 75b² = 3(9a² – 25b²)

Step 3: Recognise the difference of squares:

The expression 9a² – 25b² is a difference of squares, which can be factored as:

9a² – 25b² = (3a – 5b) (3a + 5b)

Final factorisation

So the fully factorised form is 3b(3a – 5b) (3a + 5b)