# Difference of squares special case

Created 3 years ago

Duration 0:11:19
46
Slide Content
1. ### Slide 1 - Difference of Two Squares

• Special Case!!!
2. ### Slide 2 - What you talkin’ ‘bout?!

• Sometimes, factoring the difference of two squares involves cases in which either or both squares are squares of polynomials.
• In these cases, the expression may be factored using methods similar to what we did when we factored the difference of perfect squares.
• 25a2 – (3a + 2b)2
3. ### Slide 4 - Examples:

• Factor:
• 25a2 – (3a + 2b)2
• One factor is 5a + (3a + 2b), and the other is 5a – (3a + 2b)
• 5a + (3a + 2b) = 5a + 3a + 2b = 8a + 2b = 2(4a + b) (this is done because it’s prime)
• 5a – (3a + 2b) = 5a – 3a - 2b = 2a - 2b = 2(a - b)
• So, 25a2 – (3a + 2b)2 = 2(4a + b)2(a – b)
• = 4(4a + b)(a – b) (Three factors)
4. ### Slide 6 - Example 2

• Factor:
• (3a – 2b)2 – (2a – 5b)2
• = [(3a – 2b) + (2a – 5b)][(3a – 2b) – (2a – 5b)]
• = (3a – 2b + 2a – 5b)(3a – 2b – 2a + 5b)
• = (5a – 7b)(a + 3b)