Question

Find the product:

(3x + y + 2) (3x – y + 2)

Answer 1

Given: (3x + y + 2)(3x – y + 2)

Step-wise calculation:

1. Use the distributive property to expand the product:

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

2. Calculate each term:

= 9x² – 3xy + 6x + 3xy – y² + 2y + 6x – 2y + 4

3. Combine like terms:

= 9x² + (–3xy + 3xy) + (6x + 6x) + (–y²) + (2y – 2y) + 4 

= 9x² + 0 + 12x – y² + 0 + 4

4. Final simplified expression: 

= 9x² + 12x – y² + 4