Question

(2x – 3y)³ + (3y – 4z)³ + (4z – 2x)³ can be factorised into which one of the following ?

(a) (2x + 3y + 4z) (2x – 3y – 4z) 

(b) (2x + 3y – 4z) (2x – 3y + 4z) 

(c) (2x – 3y) (3y – 4z) (4z – 2x) 

(d) 6 (2x – 3y) (3y – 4z) (2z – x)

Answer 1

(d) 6.(2x – 3y)(3y – 4z)(2z – x).

Since (2x – 3y) + (3y – 4z) + (4z – 2x) = 0, therefore, 

(2x – 3y)³ + (3y – 4z)³ + (4z – 2x)³         (Take out 2 common)

= 3.(2x – 3y)(3y – 4z) (4z – 2x) 

= 6.(2x – 3y)(3y – 4z)(2z – x).