Factorize:
Question:

Factorize:

$(5 a-7 b)^{3}+(9 c-5 a)^{3}+(7 b-9 c)^{3}$

 

Solution:

Put $(5 a-7 b)=x,(9 c-5 a)=z$ and $(7 b-9 c)=y$.

Here,

$x+y+z=5 a-7 b+9 c-5 a+7 b-9 c=0$

Thus, we have:

$(5 a-7 b)^{3}+(9 c-5 a)^{3}+(7 b-9 c)^{3}=x^{3}+z^{3}+y^{3}$

$=3 x z y \quad\left[\right.$ When $\left.x+y+z=0, x^{3}+y^{3}+z^{3}=3 x y z .\right]$

$=3(5 a-7 b)(9 c-5 a)(7 b-9 c)$

 

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