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Expanding Binomials Worksheet

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Expanding Binomials Worksheet

Expanding Binomials Worksheet

Algebraic expressions and binomial expansion illustration

📚 Part 1: FOIL Method Practice

Instructions: Use the FOIL method (First, Outer, Inner, Last) to expand each binomial product. Show all steps clearly and combine like terms to simplify your final answer.

1. Expand and simplify: (x + 3)(x + 5)
2. Expand and simplify: (x + 2)(x + 7)
3. Expand and simplify: (x - 4)(x + 6)
4. Expand and simplify: (x + 1)(x - 8)

🔢 Part 2: Binomials with Coefficients

Instructions: These problems include coefficients greater than 1. Remember to multiply all terms carefully using FOIL.

5. Expand and simplify: (2x + 3)(x + 4)
6. Expand and simplify: (3x - 2)(x + 5)
7. Expand and simplify: (2x + 1)(3x - 4)
8. Expand and simplify: (4x - 3)(2x + 7)

🌍 Part 3: Real-World Applications

Instructions: Solve these application problems using binomial expansion. Show all working clearly.

9. Garden Design Problem: A rectangular garden has dimensions of (x + 4) metres by (x + 6) metres.
a) Write an expression for the area of the garden by expanding (x + 4)(x + 6).
b) If x = 8 metres, calculate the actual area of the garden in square metres.
10. Profit Calculation: A small business sells items where the price per item is $(2x + 5) and they sell (x + 10) items per day.
a) Write an expression for the daily revenue by expanding (2x + 5)(x + 10).
b) If x = 15, calculate the daily revenue in dollars.

🎯 Part 4: FOIL Steps Check

Instructions: For the binomial product (3x - 2)(2x + 5), complete each step of the FOIL method.

11. First terms: ________________
12. Outer terms: ________________
13. Inner terms: ________________
14. Last terms: ________________
15. Write the four terms before combining like terms: ________________
16. Final simplified expression after combining like terms: ________________

💭 Part 5: Reflection

17. In your own words, explain what FOIL stands for and how you use it to expand binomials:
18. Why is it important to combine like terms after using FOIL?

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