Question

Factorise:

25(a + b)² – 36(a – b)²

Answer 1

We are given the expression:

25(a + b)² – 36(a – b)²

Step 1: Recognize it as a difference of squares

The given expression is a difference of squares.

We can apply the formula:

x² – y² = (x – y) (x + y)

Let x = 5(a + b) and y = 6(a – b)

Now, the expression becomes [5(a + b)]² – [6(a – b)]²

Step 2: Apply the difference of squares formula

= [5(a + b) – 6(a – b)] [5(a + b) + 6(a – b)]

Step 3: Simplify each factor

1. For the first factor:

5(a + b) – 6(a – b)

= 5a + 5b – 6a + 6b 

= –a + 11b

2. For the second factor:

5(a + b) + 6(a – b)

= 5a + 5b + 6a – 6b

= 11a – b

Final factorisation:

25(a + b)² – 36(a – b)²

= (–a + 11b) (11a – b)

Thus, the fully factorised form is (–a + 11b) (11a – b).