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 $\left.x+y+z=0, x^{3}+y^{3}+z^{3}=3 x y z .\right]$
$=3(5 a-7 b)(9 c-5 a)(7 b-9 c)$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.