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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.