Question
Factorize the following expressions:
(2x - 3y)3 + (4z - 2x)3 + (3y - 4z)3
(2x - 3y)3 + (4z - 2x)3 + (3y - 4z)3
✓
Answer
(2x - 3y)3 + (4z - 2x)3 + (3y - 4z)3
Let 2x - 3y = a, 4z - 2x = b, 3y - 4z = c
$\therefore$ a + b + c = 2x - 3y + 4z - 2x + 3y - 4z = 0
$\because$ a + b + c = 0
$\therefore$ a3 + b3 + c3 = 3abc
$\therefore$ (2x - 3y)3 + (4z - 2x)3 + (3y - 4z)3
= 3(2x - 3y)(4z - 2x)(3y - 4z)
Let 2x - 3y = a, 4z - 2x = b, 3y - 4z = c
$\therefore$ a + b + c = 2x - 3y + 4z - 2x + 3y - 4z = 0
$\because$ a + b + c = 0
$\therefore$ a3 + b3 + c3 = 3abc
$\therefore$ (2x - 3y)3 + (4z - 2x)3 + (3y - 4z)3
= 3(2x - 3y)(4z - 2x)(3y - 4z)
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