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)