Question

Find the product:

(x + 2y + 3) (x + 2y – 3)

Answer 1

Given: (x + 2y + 3)(x + 2y – 3)

Step-wise calculation:

1. Recognise the expression is of the form (A + B)(A – B) = A² – B².

Here, A = x + 2y and B = 3.

2. Apply the identity:

(x + 2y + 3)(x + 2y – 3) = (x + 2y)² – 3²

3. Expand (x + 2y)²:

(x + 2y)² = x² + 2 × x × 2y + (2y)²

(x + 2y)² = x² + 4xy + 4y² 

4. Calculate the square of 3:

3² = 9

5. Substitute back:

(x + 2y + 3)(x + 2y – 3) = (x² + 4xy + 4y²) – 9