Question
Factorise:
$(5 a-7 b)^3+(7 b-9 c)^3+(9 c-5 a)^3$
$(5 a-7 b)^3+(7 b-9 c)^3+(9 c-5 a)^3$
✓
Answer
Put $(5 a -7 b)= x ,(7 b-9 c )= y ,(9 c -5 a )= z$.
Here,
$x+y+z=5 a-7 b+9 c-5 a+7 b-9 c=0$
Thus,
We have:
$(5 a-7 b)^3+(9 c-5 a)^3+(7 b-9 c)^3=x^3+z^3+y^3$
$=3 x y z\left[\text { When } x+y+z=0, x^3+y^3+z^3=3 x y z\right]$
$=3(5 a-7 b)(9 c-5 a)(7 b-9 c)$
Here,
$x+y+z=5 a-7 b+9 c-5 a+7 b-9 c=0$
Thus,
We have:
$(5 a-7 b)^3+(9 c-5 a)^3+(7 b-9 c)^3=x^3+z^3+y^3$
$=3 x y z\left[\text { When } x+y+z=0, x^3+y^3+z^3=3 x y z\right]$
$=3(5 a-7 b)(9 c-5 a)(7 b-9 c)$
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