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### 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)
+ 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)
(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)
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)