Question

Proove acube-bcube = 1+3ab

Answer 1

★ Correct question:-

Prove that a³ - b³ = 1 + 3ab.

★ Answer:-

We know the algebraic identity,

x³ + y³ + z³ - 3xyz

= ( x + y + z )( x² + y² + z² - xy - yz - zx )

Now,

a³ - b³ + 1 + 3ab

= a³ + ( - b )³ + 1³ - 3 × a × ( - b ) × 1

= [ a + (-b) + 1 ] [a² + (-b)² + 1²- a(-b) - (-b)1 - 1 × a]

= ( a - b + 1 ) ( a² + b² + 1 + ab + b - a )

Hence proved!

Answer 2

The correct Question is -

Factorise

${a}^{3} - {b}^{3} + 1 + 3ab$

Solution :

${a}^{3} - {b}^{3} + 1 + 3ab \: \\ \\ = > (a - b + 1)( {a}^{2} + {b}^{2} + ab \: + b - a + 1)$