+130081 ab = 7
a^2b + ab^2 + a + b = 80
What is a^2 + b^2 ???
So we have :
a^2b + ab^2 + a + b = 80 factor the first two terms
ab (a + b) + (a + b) = 80 factor again
( a + b) (ab + 1) = 80
(a + b) (7 + 1) = 80
(a + b) (8) = 80 divide by 8 on both sides
a + b = 10
Square both sides
a^2 + 2ab + b^2 = 100
a^2 + 2(7) + b^2 = 100
a^2 + 14 + b^2 = 100 subtract 14 from both sides
a^2 + b^2 = 86
