Question

Factorise the following:

36(a + 3)² – 25(a – 2)²

Answer 1

To factorise 36(a + 3)² – 25(a – 2)² , we can treat it as a difference of squares.

First, notice that the expression is of the form A² – B², where:

A = 6(a + 3) and B = 5(a – 2)

Now, applying the difference of squares formula:

A² – B² = (A – B)(A + B)

Substitute A and B into the formula:

(6(a + 3) – 5(a – 2))(6(a + 3) + 5(a – 2)

Now simplify both terms:

1. For A – B:

6(a + 3) – 5(a – 2)

= 6a + 18 – 5a + 10

= a + 28

2. For A + B:

6(a + 3) + 5(a – 2)

= 6a + 18 + 5a – 10

= 11a + 8

Thus, the factorised form of 36(a + 3)² – 25(a – 2)² is (a + 28) (11a + 8)