Solved Examples for Difference of Two Squares


Example 1: 9x2 - 4y2

Solution:
Hence...
Rewrite 9x2 - 4y2 as a difference of two squares:         9x2 - 4y2 = (3x)2 - (2y)2
Compare (3x)2 - (2y)2 with a2 - b2:         a = 3x and b = 2y
Apply the formula a2
- b2 = (a + b)(a - b)
:
        (3x)2 - (2y)2 = (3x - 2y)(3x + 2y)
Answer: (3x - 2y)(3x
+ 2y)


Example 2: a2 - 9b2

Solution:
Hence...
Rewrite a2 - 9b2 as a difference of two squares:       a2 - 9b2 = a2 - (3b)2
Compare a2 - (3b)2 with
a2 - b2
:
      a = a and b = 3b
Apply the formula a2
- b2 = (a + b)(a - b)
:
      a2 - (3b)2 = (a + 3b)(a - 3b)
Answer: (a + 3b)(a - 3b)


Example 3: 4x2 - 25y2

Solution:
     Hence...
Rewrite 4x2 - 25y2 as a difference of two squares:       4x2 - 25y2 = (2x)2 - (5y)2
Compare (2x)2 - (5y)2 with
a2 - b2
:
      a = 2x and b = 5y
Apply the formula a2
- b2 = (a + b)(a - b)
:
      (2x)2 - (5y)2 = (2x + 5y)(2x - 5y)
Answer: (2x + 5y)(2x - 5y)


Example 4: x2 - 1

Solution:
     Hence...
Rewrite x2 - 1 as a difference of two
squares
     x2 - 12
Compare x2 - 12 with a2 - b2     a
= x and b = 1
Apply the formula a2 - b2 = (a + b)(a - b)x2 - 12 = (x + 1)(x - 1)
Answer:
(x + 1)(x - 1)


Example 5: 3x2 - 3

Solution:
     Hence...
Take 3 as the common factor:      3(x2 - 1)
Rewrite 3(x2 - 1) as a difference of two squares:      3(x2 - 12)
Compare x2 - 12 with a2 - b2: a = x and b = 1
Apply the formula a2 - b2 = (a + b)(a - b): 3(x2 - 12) = 3(x + 1)(x - 1)
Answer:
3(x + 1)(x - 1)


Example 6: x^2/4 - 1/4
Solution:
     Hence...
Rewrite the given expression as a difference of two squares:      


Compare


with a2 - b2:
     

Apply the formula a2 - b2 = (a + b)(a - b):

Answer: a2 - b2 = (a + b)(a - b)