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Multiplying Binomials with FOIL

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Lesson Details

Grade Level
9-12
Duration (minutes)
2
Summary
A Grade 9-12 math lesson teaching students how to multiply two binomials using the FOIL method (First, Outer, Inner, Last), which organizes the distributive property, with two fully worked examples showing how to multiply the four term pairs and combine like terms.

FOIL method reference showing First, Outer, Inner, Last, with two worked examples: (x + 3)(x + 5) multiplied to get x squared plus 8x plus 15, and (2x - 1)(x + 4) multiplied to get 2x squared plus 7x minus 4

Student Worksheet: Multiplying Binomials with FOIL

Teacher Note: Students can watch the video lesson above and answer the questions. Click the “Teacher Answer Key” dropdown below when you are ready to review the solutions!

Key Concepts:

• Binomial: An expression with two terms, like x + 3.

• FOIL: Stands for First, Outer, Inner, Last — a way to organize the distributive property when multiplying two binomials.

• The Four Products: Multiply the first terms, the outer terms, the inner terms, and the last terms, then write all four products together.

• Combining Like Terms: After FOIL, combine any terms with the same variable and exponent to write the final simplified answer.

Instructions: Read each question carefully and write your answer in the space provided.

  1. Question 1: What does FOIL stand for?
  2. Question 2: Multiply (x + 3)(x + 5) using FOIL. Show all four products before combining like terms.
  3. Question 3: Combine the like terms from Question 2 to write the final answer.
  4. Question 4: Multiply (2x − 1)(x + 4) using FOIL. Show all four products before combining like terms.
  5. Question 5: Combine the like terms from Question 4 to write the final answer.
Click to reveal Teacher Answer Key

1. First, Outer, Inner, Last.

2. First: x × x = x². Outer: x × 5 = 5x. Inner: 3 × x = 3x. Last: 3 × 5 = 15.

3. x² + 5x + 3x + 15 = x² + 8x + 15.

4. First: 2x × x = 2x². Outer: 2x × 4 = 8x. Inner: −1 × x = −x. Last: −1 × 4 = −4.

5. 2x² + 8x − x − 4 = 2x² + 7x − 4.

Disclaimer: This worksheet was generated with AI assistance based on original video content. It is intended for educational reference only. Teachers are encouraged to review and adjust questions to fit their curriculum standards before classroom use.

🎯 Extension Activity: Multiply (x + 2)(x − 6) using FOIL. Then multiply (3x + 1)(x − 2). Show all four products and combine like terms for both.

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