Simplify the following (2x – y + 3) (2x – y – 3)

(i) (2x – y + 3) (2x – y – 3)

(ii) (3x + y – 5) (3x – y – 5)

Answer :

(i) (2x – y + 3) (2x – y – 3)

It can be written as

= [(2x – y) + 3] [(2x – y) – 3]

= (2x – y)² – 3²

By further calculation

= (2x)² +y² – 2 × 2x × y – 9

So we get

= 4x² + y² – 4xy – 9

(ii) (3x + y – 5) (3x – y – 5)

It can be written as

= [(3x – 5) + y] [(3x – 5) – y]

= (3x – 5²) – y²

By further calculation

= (3x)² + 5² – 2 × 3x × 5 – y²

So we get

= 9x² + 25 – 30x – y²

= 9x² – y² – 30x + 25

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