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In **Algebra 1**, multiplying binomials using the **FOIL method** is a structured way to expand the product of two binomials. FOIL stands for **First, Outer, Inner, Last**, which represents the order in which terms are multiplied.
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### **FOIL Method**
For two binomials, \( (a + b)(c + d) \), follow these steps:
1. **First**: Multiply the first terms in each binomial: \( a \cdot c \).
2. **Outer**: Multiply the outer terms in the product: \( a \cdot d \).
3. **Inner**: Multiply the inner terms in the product: \( b \cdot c \).
4. **Last**: Multiply the last terms in each binomial: \( b \cdot d \).
Combine all results and simplify by adding like terms.
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### **Examples**
1. **Expand \( (x + 3)(x + 5) \)**:
- **First**: \( x \cdot x = x^2 \)
- **Outer**: \( x \cdot 5 = 5x \)
- **Inner**: \( 3 \cdot x = 3x \)
- **Last**: \( 3 \cdot 5 = 15 \)
- Combine: \( x^2 + 5x + 3x + 15 = x^2 + 8x + 15 \).
- **Answer**: \( x^2 + 8x + 15 \).
2. **Expand \( (2x - 1)(x + 4) \)**:
- **First**: \( 2x \cdot x = 2x^2 \)
- **Outer**: \( 2x \cdot 4 = 8x \)
- **Inner**: \( -1 \cdot x = -x \)
- **Last**: \( -1 \cdot 4 = -4 \)
- Combine: \( 2x^2 + 8x - x - 4 = 2x^2 + 7x - 4 \).
- **Answer**: \( 2x^2 + 7x - 4 \).
3. **Expand \( (x - 3)(x - 2) \)**:
- **First**: \( x \cdot x = x^2 \)
- **Outer**: \( x \cdot -2 = -2x \)
- **Inner**: \( -3 \cdot x = -3x \)
- **Last**: \( -3 \cdot -2 = 6 \)
- Combine: \( x^2 - 2x - 3x + 6 = x^2 - 5x + 6 \).
- **Answer**: \( x^2 - 5x + 6 \).
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### **Practice Problems**
1. Expand \( (x + 2)(x + 7) \).
2. Expand \( (3x - 4)(x + 5) \).
3. Expand \( (x - 6)(x - 3) \).
4. Expand \( (2x + 1)(x - 3) \).
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### **Tips**
- Always multiply systematically using FOIL.
- Combine like terms carefully.
- Double-check signs, especially when multiplying negatives.
I have many informative videos for Pre-Algebra, Algebra 1, Algebra 2, Geometry, Pre-Calculus, and Calculus. Please check it out:
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Nick Perich
Norristown Area High School
Norristown Area School District
Norristown, Pa
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