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`
This is the answer.
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`
This is the answer
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`
This is the answer.
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