Simplify the following (3p – 4q) (9p2 + 12pq + 16q2)

(i) (3p – 4q) (9p² + 12pq + 16q²)

(ii) (x – 3/x) (x² + 3 + 9/x²)

Answer :

(i) (3p – 4q) (9p² + 12pq + 16q²)

It can be written as

= (3p – 4q) [(3p)² + 3p × 4q + (4q)²]

By further simplification

= (3p)³ – (4q)³

= 27p³ – 64q³

(ii) (x – 3/x) (x² + 3 + 9/x²)

It can be written as

= (x – 3/x) [x² + x × 3/x + (3/x)²]

By further simplification

= x³ – (3/x)³

= x³ – 27/x³

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