Question

9x² – 36y² is equal to ______.

Options

• (3x + 6y) (3x – 6y)

• (3x – 6y)²

• 9(x + 2y) (x – 2y)

• 9(x – 6y)²

Answer 1

9x² – 36y² is equal to 9(x + 2y) (x – 2y).

Explanation:

The expression 9x² – 36y² is a difference of squares.

We can factor it as follows:

9x² – 36y² = 9(x² – 4y²)

Now, x² – 4y² is a difference of squares, which factors as x² – 4y² = (x + 2y) (x – 2y).

Thus, the full factorisation is 9(x² – 4y²) = 9(x + 2y) (x – 2y).