The GCF of two numbers p + q is 5. What is the GCF of p² + q²? Explain your answer.

Answer 1

p=5k

q=5m

p^2 = 25k^2

q^2 = 25m^2

GCF is 25

try a couple simple examples, p=5, q=10

square them: 25 and 100, GCF is 25.

or p=15 and q= 35, put them in prime form: 3(5), 7(5), GCF =5

square them: 225 and 1225. put them in prime factors

5(5)(3)(3) and 5(5)(7)(7) GCF is 5(5) =25