Find the value of 8a3 – 27b3.

If 2a – 3b = 3 and ab = 2, find the value of 8a³ – 27b³.

Answer :

We know that

8a³ – 27b³ = (2a)³ – (3b)³

According to the formula

= (2a – 3b)³ + 3 × 2a × 3b (2a – 3b)

By further simplification

= (2a – 3b)³ + 18ab (2a – 3b)

Substituting the values

= 3³ + 18 × 2 × 3

By further calculation

= 27 + 108

= 135

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