Question

factorise 8 x ^3 + y ^3-27 Z ^3 + 18 x y z​

Answer 1

Answer:

(2x + y - 3z)(4x² + y² + 9z² - 2xy + 3yz + 6xz)

Step-by-step explanation:

Given :

To factorize the expression,

8x³ + y³ - 27z³ + 18xyz

Solution :

The expression,

8x³ + y³ - 27z³ + 18xyz  is of the form,

a³ + b³ + c³ - 3abc,

where,

a = 2x , b = y , c = -3z,.

i.e., (2x)³ + (y)³ + (-3z)³ - 3(2x)(y)(-3z)

We know that,

a³ + b³ + c³ - 3abc = ( a + b + c ) ( a² + b² + c² - 2ab - 2ac - 2bc )

By substituting the values,

we get,

8x³ + y³ - 27z³ + 18xyz = (2x)³ + (y)³ + (-3z)³ - 3(2x)(y)(-3z)

⇒ ( 2x + y - 3z ) ( (2x)² + (y)² + (-3z)² - 2(2x)(y) - 2(y)(-3z) - 2(2x)(-3z) )

⇒ (2x + y - 3z)(4x² + y² + 9z² - 2xy + 3yz + 6xz)