Question

resolved a^3 - b^3 + 1 + 3ab in to factor

Answer 1

Hi ,

a³ - b³ + 1 + 3ab

= [ a³ + ( -b )³ + 1³ ] + 3ab

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we know the algebraic identity

x³ + y³ + z³ = (x + y+z ) (x²+y²+z²-xy-yz-zx)+3xyz

************************************

= {( a - b + 1 )[ a² + b² + 1² + ab +b - a] - 3ab} +3ab

= ( a - b + 1 )( a² + b² + 1 + ab + b - a ) - 3ab + 3ab

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

I hope this helps you.

:)

Answer 2

Answer:

a³ - b³ + 1 + 3ab

= [ a³ + ( -b )³ + 1³ ] + 3ab

********************

we know the algebraic identity

x³ + y³ + z³ = (x + y+z ) (x²+y²+z²-xy-yz-zx)+3xyz

************************************

= {( a - b + 1 )[ a² + b² + 1² + ab +b - a] - 3ab} +3ab

= ( a - b + 1 )( a² + b² + 1 + ab + b - a ) - 3ab + 3ab

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

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