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### Solved Examples: Square of a Sum (a + b)^2

#### Solved Example 1

Expand the expression (x + 2y)^2

#### Solution

Compare the given expression (x + 2y)^2 with the expansion formula (a + b)^2. We get
a = x and b = 2y
Write down the expansion formula
(a + b)^2 = a^2 + b^2 + 2ab
Put 'x' in place of 'a' and '2y' in place of 'b' in the above formula
(x + 2y)^2 = (x)^2 + (2y)^2 + 2(x)(2y)
Simplify the right hand side.
(x + 2y)^2 = x^2 + 4y^2 + 4xy

#### Solved Example 2

Expand the expression (2a + 3b)^2

#### Solution

Compare the given expression (2a + 3b)^2 with the expansion formula (a + b)^2. We get
a = 2a and b = 3b
Write down the expansion formula
(a + b)^2 = a^2 + b^2 + 2ab
Put '2a' in place of 'a' and '3b' in place of 'b' in the above formula
(2a + 3b)^2 = (2a)^2 + (3b)^2 + 2(2a)(3b)
Simplify the right hand side.
(2a + 3b)^2 = 4a^2 + 9b^2 + 12ab

#### Solved Example 3

Expand the expression (x/2 + y/3)^2

#### Solution

Compare the given expression (x/2 + y/3)^2 with the expansion formula (a + b)^2. We get
a = x/2 and b = y/3
Write down the expansion formula
(a + b)^2 = a^2 + b^2 + 2ab
Put 'x/2' in place of 'a' and 'y/3' in place of 'b' in the above formula
(x/2 + y/3)^2 = (x/2)^2 + (y/3)^2 + 2(x/2)(y/3)
Simplify the right hand side.
(x/2 + y/3)^2 = x^2/4 + y^2/9 + (xy)/3