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

(i) (x + 2/x – 3) (x – 2/x – 3)

(ii) (5 – 2x) (5 + 2x) (25 + 4x²)

Answer :

(i) (x + 2/x – 3) (x – 2/x – 3)

It can be written as

= [(x – 3) + (2/x)] [(x – 3) – (2/x)]

= (x – 3)² – (2/x)²

Expanding using formula

= x² + 9 – 2 × x × 3 – 4/x²

By further calculation

= x² + 9 – 6x – 4/x²

So we get

= x² – 4/x² – 6x + 9

(ii) (5 – 2x) (5 + 2x) (25 + 4x²)

It can be written as

= [5² – (2x)²] (25 + 4x²)

By further calculation

= (25 – 4x²) (25 + 4x²)

So we get

= 25² – (4x²)²

= 625 – 16x⁴

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