Expand the polynomial:

(5a+1/5 b) ^2

Replaced A for X and B for Y

(25x^2) + (2xy) + (y^2/25)

Expand the following:

(5 a + b/5) ^2

(5 a + b/5) (5 a + b/5) = (5 a) (5 a) + (5 a) (b/5) + (b/5) (5 a) + (b/5) (b/5):

5*5 a a + (5 a b) / 5 + (5 b a) / 5 + (b b) / (5*5)

(5 a b) / 5 = 5/5*a b = a b:

5*5 a a + a b + (5 b a) / 5 + (b b) / (5*5)

(b*5 a) / 5 = 5/5*b a = b a:

5*5 a a + a b + b a + (b b) / (5*5)

Combine powers. (b b) / (5*5) = (b^ (1 + 1)) / (5*5):

5*5 a a + a b + b a + (b^ (1 + 1)) / (5*5)

1 + 1 = 2:

5*5 a a + a b + b a + (b^2/5) / 5

5 a*5 a = 5*5 a^2:

5*5 a^2 + a b + b a + (b^2/5) / 5

5*5 = 25:

Answer: 25 a^2 + a b + b a + (b^2/5) / 5