1. Factoring binomials

2. Difference of Two Squares
Always check for a GCF
Only for subtraction
Each term must be a perfect square
The exponents on the variables must be even
Numbers that are Perfect Squares:
1² = 1, 2² = 4, 3² = 9, 4² = 16, 5² = 25, 6² = 36, 7² = 49, 8² = 64, 9² = 81, 10² = 100, 11² = 121, 12² = 144, etc

3. a² - b² = (a + b)(a – b) Example: x² - 16
a² = x² b² = 16 (positive value)
A = x b = 4
Answer: (x + 4)(x – 4)
Example: 25x² - 1
a² = 25x² b² = 1
A = 5x b = 1
Answer: (5x + 1)(5x – 1)

4. Practice 16y² - 49g² P⁸ - 81 d⁶ - c⁴ x² + 4 (4y – 7g)(4y + 7g)
(p⁴ + 9)(p⁴ - 9)
(d³ - c²)(d³ + c²)
prime

5. Look out for Tricks Example: 48x⁵ -3x³ GCF: 3x³(16x² - 1)
Answer: 3x³(4x – 1)(4x + 1)
Example: x² + 100
Rewrite: x²
Answer: (10 -3x)(10 +3x)
Example: c² - (9/25)
a² = c² b² = 9/25
a = c b = 3/5
Answer: (c – 3/5)(c + 3/5)

6. Sum and Difference of 2 Cubes
Always check for a GCF
Each term must be a perfect cube
The exponents on the variables must be divisible by three (3, 6, 9, 12, 15, 18, etc)
Numbers that are Perfect Cubes:
1³ = 1, 2³ = 8, 3³ = 27, 4³ = 64, 5³ = 125,
6³ = 216, 7³ = 343, 8³ = 512, 9³ = 729, 10³ = 1000

7. a³ + b³ = (a +b)(a² - ab + b²) a³ - b³ = (a - b)(a² + ab + b²)
Example: x³ + 8
a³ = x³ b³ = 8
a = x b = 2
(x + 2) ((x) ² - (x)(2) + (2) ²)
Answer: (x + 2)(x² - 2x + 4)
Example: x³ + 27
Answer: (x + 3)(x² - 3x + 9)

8. Example: 125a³ - 1
a³ = 125a³ b³ = 1
a = 5a b = 1
(5a-1)((5a)² + (5a)(1) + 1²)
Answer: (5a – 1)(25a² + 5a + 1)
Example: 16x³ - 250y³
GCF: (8x³ - 125y³)
Answer: 2(2x – 5y)(4x² + 10xy + 25y²)

9. Practice 8g³ - 64 X³ + 1000 5k³ - 40 6y³z + 48x⁶z
(2g – 4)(4g² + 8g + 16)
(x + 10)(x² - 10x + 100)
5(k – 2)(k² + 2k + 4)
6z(y + 2x²)(y² - 2x²y + 4x)⁴