Question

Factorize: 2√2a3 + 8b3 -27c3 + 18√2 abc

Answer 1

Answer:

(√2a + 2b-3c) ( 2a² + 4b²+9c²-2√2ab +6bc+3√2ca )

Step-by-step explanation:

let Z=2√2a³ + 8b³ -27c³ + 18√2 abc

We can write this expression as:

Z=(√2a)³ + (2b)³+(-3c)³-3*(√2a)(2b)(-3c)

let √2a =x,2b=y and -3c=z then

Z= x³+y³+z³-3xyz

Z=(x+y+z) ( x²+y²+z²-xy-yz-zx)

Putting back the values of x,y and z we get

Z= (√2a + 2b-3c) { (√2a)² + (2b)²+(-3c)²-(√2a)(2b) -(2b)(-3c)-(-3c)(√2a) }

Z=  (√2a + 2b-3c) ( 2a² + 4b²+9c²-2√2ab +6bc+3√2ca )