Question

Factorise:

(y² + 3)² – 16y²

Answer 1

We are asked to factorise:

(y² + 3)² – 16y²

Step 1: Recognise it as a difference of squares:

This is a difference of squares, which follows the formula:

a² – b² = (a – b) (a + b)

Let a = (y² + 3) and b = 4y

Now the expression becomes [(y² + 3)]² – (4y)²

Step 2: Apply the difference of squares formula:

= (y² + 3 – 4y) (y² + 3 + 4y)

Step 3: Simplify each factor:

1. For the first factor

y² + 3 – 4y = y² – 4y + 3

2. For the second factor:

y² + 3 + 4y = y² + 4y + 3

Final factorisation

(y² + 3)² – 16y² = (y² – 4y + 3) (y² + 4y + 3)

Thus, the fully factorised form is (y² – 4y + 3) (y² + 4y + 3)