1.

Find the value of : `(i) x^(3)+y^(3)-12xy+64`, when x+y=-4 `(ii) x^(3)-8y^(3)-36xy-216`, when x=2y+6

Answer» `(i) x^(3)+y^(3)-12xy+64=x^(3)+y^(3)+4^(3)-3x xx y xx4`
`=(x+y+4)(x^(2)+y^(2)+4^(2)-xy-4y-4x)`
`=(0)(x^(2)+y^(2)+4^(2)-xy-4y-4x)=0`
`(ii) x^(3)-8y^(3)-36xy-216=x^(3)+(-2y)^(3)+(-6)^(3)-3x(-2y)(-6)`
`=(x-2y-6)[x^(2)+4y^(2)+36+2xy-12y+6x)`
`=(0)(x^(2)+4y^(2)+36+2xy-12y+5x)=0 " " (because x=2y+6)`


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