More Complex Binomial Products Worksheet — Algebra Practice for 13-Year-Olds

Instructions

Expand and simplify each expression below. Remember to use the FOIL method (First, Outer, Inner, Last) for multiplying two binomials. After multiplying, always check if there are any like terms you can combine to simplify your final answer!

Warm-up: The Basics

Let's refresh our memory of the FOIL method.

1. (x + 3)(x + 7)
2. (a - 5)(a + 2)

Part A: Working with Coefficients

These binomials have numbers (coefficients) in front of the variables. Be careful with your multiplication!

1. (2x + 1)(x + 5)
2. (3y - 4)(2y + 3)
3. (5m - 2)(4m - 1)
4. (-3p + 5)(p - 6)

Part B: Spot the Special Cases!

Look for these common patterns to work more efficiently:

• Perfect Square: (a + b)² = a² + 2ab + b²
• Perfect Square: (a - b)² = a² - 2ab + b²
• Difference of Squares: (a + b)(a - b) = a² - b²

1. (x + 8)²
2. (3y - 2)²
3. (k + 11)(k - 11)
4. (4a + 5b)(4a - 5b)

Part C: Juggling Multiple Variables

The same FOIL rules apply when you have more than one type of variable. Watch for like terms!

1. (x + 2y)(x + 4y)
2. (3a + b)(2a - 5b)
3. (5c - 2d)(3c - d)
4. (2m + 3n)²

Challenge Zone

Ready for a real test? To solve this, multiply the first two binomials together. Then, take your resulting expression and multiply it by the third binomial.

1. (x + 2)(x - 1)(x + 3)

Answer Key

Warm-up: The Basics

1. x² + 10x + 21
2. a² - 3a - 10

Part A: Working with Coefficients

1. 2x² + 11x + 5
2. 6y² + y - 12
3. 20m² - 13m + 2
4. -3p² + 23p - 30

Part B: Spot the Special Cases!

1. x² + 16x + 64
2. 9y² - 12y + 4
3. k² - 121
4. 16a² - 25b²

Part C: Juggling Multiple Variables

1. x² + 6xy + 8y²
2. 6a² - 13ab - 5b²
3. 15c² - 11cd + 2d²
4. 4m² + 12mn + 9n²

Challenge Zone

1. x³ + 4x² + x - 6