1.

Factorise a^3b^3-64 (a+b)^3​

Answer»

★ ANSWER :

To factorise :

a³b³ - 64(a + b)³

Solution :

a³b³ = (ab)³

64 = 4³

64(a+ b)³ = 4³(a+b)³

= {4(a+b)}³ = (4a + 4b)³

SIMPLIFIED FORM :

factorise :

(ab)³ - (4a + 4b)³

We know that ,

a³ - b³ = (a - b) (a² + ab + b²)

by using the formula

(ab)³ - (4a + 4b)³

{(ab) - (4a + 4b)} {(ab)² + (ab)(4a + 4b) + (4a + 4b)² }

identity -

(a +b)² = a² + 2ab + b²

(ab - 4a - 4b) {a²b² + 4a²b + 4ab² + 16a² + 16b² + 32ab }

→ (ab - 4a - 4b) (a²b² + 4a²b + 4ab² + 16a² + 16b² + 32ab)


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