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