Simplify the following (3x – 1)2 – (3x – 2) (3x + 1)

(i) (3x – 1)² – (3x – 2) (3x + 1)

(ii) (4x + 3y)² – (4x – 3y)² – 48xy

Answer :

(i) (3x – 1)² – (3x – 2) (3x + 1)

It can be written as

= [(3x)² + 1² – 2 × 3x × 1] – [(3x)² – (2 – 1) (3x) – 2 × 1]

By further calculation

= [9x² + 1 – 6x] – [9x² – 3x – 2]

So we get

= 9x² + 1 – 6x – 9x² + 3x + 2

= -3x + 3

= 3 – 3x

(ii) (4x + 3y)² – (4x – 3y)² – 48xy

It can be written as

= [(4x)² + (3y)² + 2 × 4x × 4y] – [(4x)² + (3y)² – 2 × 4x × 3y] – 48xy

By further calculation

= [16x² + 9y² + 24xy] – [16x² + 9y² – 24xy] – 48xy

So we get

= 16x² + 9y² + 24xy – 16x² – 9y² + 24xy – 48xy

= 0

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