Question

if x=2y+6 then find the value of x cube- 8y cube -36xy-216

Answer 1

x = 2y + 6
⇒ x - 2y = 6
⇒ (x-2y)³ = 6³
⇒ x³ - (2y)³ - 3 × x × 2y (x-2y) = 216
⇒ x³ - 8y³ - 3 × x × 2y (6) = 216
⇒ x³ - 8y³ - 36xy = 216
⇒ x³ - 8y³ - 36xy - 216 = 216-216
⇒ x³ - 8y³ - 36xy - 216 = 0

Answer 2

x=2y+6
x-2y-6=0

x³-8y³-(36xy)³-216 
=x³+(-2y)³+(-6)³-3 × x × -2y × -6
=(x-2y-6) (x²+6x-12y+2xy+4y²+36)
=0