# math

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

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1. x^3-8y^3-36xy-216
(x-2y)(x^2+2xy-4y^2)-72y^2-108-216
(6)(4y^2-24y+4y^2)-72y^2-324
check those lines carefully, I did them in my head. If correct, then combine terms...

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bobpursley
2. [x^3-8y^3] -36xy-216
= (x - 2y)(x^2 + 2xy + 4y^2) - 36(xy + 6)
= 6((2y+6)^2 + 2y(2y+6) + 4y^2) - 36(y(2y+6) + 6)
= 6( 4y^2 + 24y + 36 + 4y^2 + 12y + 4y^2) - 36(2y^2 + 6y + 6)
= 24y^2 + 144y + 216 + 24y^2 + 72y + 24y^2 - 72y^2 - 216y - 216
= 0

check:
let y = 1, then x = 8

x^3 - 8y^3 - 36xy - 216
= 512 - 8 - 288 - 216 = 0
= 0

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