Question

If 2a+b+3c = 0, then 8a3+b3+27c3 is ....

Answer 1

Step-by-step explanation:

Given that :2a+b+3c=0

=>2a+b=-3c --------(1)

Cubing on both sides then

(2a+b)³=(-3c)³

We know that (a+b)³=a³+3ab(a+b)+b³

Here , a=2a and b=b

=>(2a)³+3(2a)(b)(2a+b)+b³=-27c³

=>8a³+6ab(2a+b)+b³=-27c³

=>8a³+b³+6ab(-3c)=-27c³ (from(1))

=>8a³+b³-18abc=-27c³

=>8a³+b³+27c³=18abc

(or)

We know that

a+b+c=0 then a³+b³+c³=3abc

here a=2a;b=b;c=3c

it is given that

2a+b+3c=0

=>(2a)³+b³+(3c)³=3(2a)(b)(3c)

=>8a³+b³+27c³=18abc