Question

It is given that $3a+2b=5c,$ then find the value of $27a^3+8b^3-125c^3$ if $abc=0.$

Answer 1

Given: $3a+2b=5c$

$3a+2b-5c=0\dots \dots \left(i\right)$

We know that $x^3+y^3=(x+y{)}^3-3xy(x+y)$

Now, $27a^3+8b^3-125c^3=(3a{)}^3+(2b{)}^3+(-5c{)}^3$

$=(3a+2b{)}^3-3(3a\left)\right(2b\left)\right(3a+2b)-125c^3$ [$x^3+y^3=(x+y{)}^3-3xy(x+y)$]

$=(5c{)}^3-18ab(5c)-(5c{)}^3$ From given

$=18abc$

$=\left(18\right)\times 0$ [Given that $abc=0$]

$=0$