X + y = 3, xy = 1, a + B = 5, ab = 3, M = ax + BX, n = BX + ay, find the value of M3 + N3 Why?

Is m = ax + by?
If so, then
m+n=ax+ay+bx+by
=a(x+y)+b(x+y)
=(x+y)(a+b)
=15
mn=abx^2+a^2xy+b^2xy+aby^2
=ab(x^2+y^2)+xy(a^2+b^2)
=ab[(x+y)^2-2xy]+xy[(a+b)^2-2ab]
=3*(9-2)+1*(25-6)
=40
So m ^ 3 + n ^ 3 = (M + n) (m ^ 2 + n ^ 2-MN)
=(m+n)[(m+n)^2-3mn]
=15*(15^2-3*40)
=1575

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