Question

a cube minus b cube + 1 + 3 ab factorise​

Answer 1

Hi ,

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We know the algebraic identity ,

x³ + y³ + z³ - 3xyz

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

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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 )

I hope this helps you.