Factorize each of the following expressions:
(2x-3y)³+(4z-2x)³+(3y-4z)³
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The algebraic expression is given as : (2x - 3y)³ + (4z - 2x)³ + (3y - 4z)³
Let 2x – 3y = a , 4z – 2x = b , 3y – 4z = c. Then
a + b + c = 3x − 2y + 2y − 4z + 4z − 3x = 0
We know, a³ + b³ + c³− 3abc = (a + b + c)(a² + b² + c²− ab − bc − ca)
∴ a³ + b³ + c³ = 3abc
⇒ (2x - 3y)³ + (4z - 2x)³ + (3y - 4z)³ = 3(2x − 3y)(4z − 2x)(3y − 4z)
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Answer:
Step-by-step explanation:
Let 2x – 3y = a , 4z – 2x = b , 3y – 4z = c. Then
a + b + c = 3x − 2y + 2y − 4z + 4z − 3x = 0
We know, a³ + b³ + c³− 3abc = (a + b + c)(a² + b² + c²− ab − bc − ca)
∴ a³ + b³ + c³ = 3abc
⇒ (2x - 3y)³ + (4z - 2x)³ + (3y - 4z)³ = 3(2x − 3y)(4z − 2x)(3y − 4z)
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