Question

if x=2y+6,prove x^3-8y^3-36xy-212=4

Answer 1

Hey there !!!!

x=2y+6

x-2y=6--------Equation 1

cubing equation 1 on both sides

(x-2y)³=6³

(a-b)³= a³-3a²b+3ab²-b³

In (x-2y)³ a =x b=2y

So,
(x-2y)³= x³-3x²*2y+3*x*(2y)²-(2y)³=6³

(x-2y)³=x³-6x²y+12xy²-8y³=216

           x³-6x²y+12xy²-8y³=212+4

           x³-8y³ -6x²y+12xy²-4=212

           x³-8y³ +6xy(2y-x)-4=212
        
            x³-8y³ +6xy(2y-x)-4=212

             x³-8y³ +6xy(2y-x)-4=212  ------------Equation 2


But x=2y+6 ⇒⇒⇒ 2y-x= -6

   Substituting 2y-x = -6 in equation 2        


    x³-8y³ +6xy(-6)-4=212   

    x³-8y³-36xy-4=212  

Hope this helped you.............