Question

Factorise : 27x3 + y3 + 2? - 9xyz​

Answer 1

Gívєn :

• Factorise : 27x3 + y3 + 2? - 9xyz

Sσlutíσn :

➛ 27x³ + y³ + z³ - 9xyz

➛ (3x)³ + (y)³ + (z)³ - 9xyz

➛ $\bf{(3x)^3 + (y)^3 + (z)^3 - 3 × 3x × y × z}$

${\boxed{\green{\sf{Using \: identity}}}}$

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

➛ Putting a = 3x, b = y, c = z

➛$\bf{(3x)^3 + (y)^3 + (z)^3 - 3 × 3x × y × z}$

Answer 2

Solution:-

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)] [Since (a + b + c )(a2 + y2 + z2 - ab−bc−ca)] = [3x + y + z ][9x2 + y2 + z2 - 3xy − yz − 3zx]