Question

64m³-216n³ solve using suitable identity.
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Answer 1

1st Method.

Given :-

= 64m³ - 216n³

= (4m)³ - (6n)³

As this is in the form form of a³ - b³ and we know a Identity i.e.

a³ - b³ = (a-b) (a² + b² + ab)

(4m)³ - (6n³) = (4m-6n) [(4m)² + (6n)² + 4m.6n]

(4m)³ - (6n)³ = (4m-6n)(16m² + 36n² + 24mn)

2nd Method.

(a-b)³ = a³ - b³ - 3ab(a-b)

(a-b)³ + 3ab(a-b) = a³ - b³

(4m)³ - (6n)³ = (4m-6n)³ + 3.4m.6n(4m-6n)

(4m)³ - (6n)³ = (4m-6n)³ + 72mn(4m-6n)