What is two times the sum of x squared and y squared increase by three times the sum of x squared and y squared?

To find two times the sum of ( x^2 ) and ( y^2 ) increased by three times the sum of ( x^2 ) and ( y^2 ), we first express it mathematically. The sum of ( x^2 ) and ( y^2 ) is ( x^2 + y^2 ). Thus, two times this sum is ( 2(x^2 + y^2) ), and three times it is ( 3(x^2 + y^2) ). Adding these together gives ( 2(x^2 + y^2) + 3(x^2 + y^2) = 5(x^2 + y^2) ).