Question

Expand the following:

(2x – 3y + 1) (2x – 3y – 5)

Answer 1

Given: (2x – 3y + 1)(2x – 3y – 5)

Stepwise calculation:

Use distributive property (FOIL method) to expand:

(2x – 3y + 1)(2x – 3y – 5) = (2x)(2x – 3y – 5) – (3y)(2x – 3y – 5) + 1(2x – 3y – 5)

Calculate each part:

1. (2x)(2x – 3y – 5) = 2x × 2x – 2x × 3y – 2x × 5

(2x)(2x – 3y – 5) = 4x² – 6xy – 10x

2. –(3y)(2x – 3y – 5) = –3y × 2x + 3y × 3y + 3y × 5

–(3y)(2x – 3y – 5) = –6xy + 9y² + 15y

3. 1(2x – 3y – 5) = 2x – 3y – 5

Now sum these results:

4x² – 6xy – 10x – 6xy + 9y² + 15y + 2x – 3y – 5

Combine like terms:

For (x²): (4x²)

For (xy): (–6xy – 6xy = –12xy)

For (x): (–10x + 2x = –8x)

For (y²): (9y²)

For (y): (15y – 3y = 12y)

Constant term: (–5)

(2x – 3y + 1)(2x – 3y – 5) = 4x² – 12xy – 8x + 9y² + 12y – 5