Given that x + y = 3, a + B = 5, xy = 1, ab = 3, and M = ax + by, n = BX + ay, find the square of M times the square of n

Given that x + y = 3, a + B = 5, xy = 1, ab = 3, and M = ax + by, n = BX + ay, find the square of M times the square of n

x+y=3,a+b=5,xy=1,ab=3,m=ax+by,n=bx+ay
m²+n²=(ax+by)²+(bx+ay)²=x²(a²+b²)+y²(a²+b²)+4xyab
=(x²+y²)(a²+b²)+4*(xy)(ab)
=[(x+y)²-2xy][(a+b)²-2ab]+4*1*3
=(9-2)(25-2*3)+12
=7*19+12
=145
A: 145

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