Factorise:

27x^3+y^3+z^3-9xy

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Solution

Consider, 27x³+ y³ + z3- 9xyz

= (3x)³+ y³ + z³ - 3 × (3x) × y × z

= [3x + y + z ][(3x)² + y² + z² - (3x) × y − y × z − z(3x)]

a³+b³+c³-3abc = (a + b + c )(a²+ b²+ c² - ab−bc−ca)

putting a=3x ,b=y ,c=z

= [3x + y + z ][9x² + y²+ z²- 3xy − yz − 3zx]

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