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Solved Example 1

Expand the expression `(x + 2y)^2`

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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`

This is the answer.

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Solved Example 2

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

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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`

This is the answer

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Solved Example 3

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

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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`

This is the answer.

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