Solved Examples: Square of a Difference `(a - b)^2`

Solved Example 1

Expand `(2x - 3y)^2`

Solution

Compare the given expression with the expansion formula `(a - b)^2`. We get

`a = 2x` and `b = 3y`

Write down the expansion formula

`(a - b)^2 = a^2 + b^2 - 2ab`

Put '2x' in place of 'a' and '3y' in place of 'b' in the above formula

`(2x - 3y)^2 = (2x)^2 + (3y)^2 - 2(2x)(3y)`

Simplify the right hand side.

`= 4x^2 + 9y^2 - 12xy`

This is the answer.

Solved Example 2

Expand `(x/2 - y/3)^2`

Solution

Compare the given expression 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^2/4 + y^2/9 - (xy)/3`

This is the answer.