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Understanding the FOIL Method for Multiplying Binomials

Learn how to multiply binomials using the FOIL method, a vital technique in polynomial algebra. FOIL stands for First, Outside, Inside, Last, guiding you through the multiplication process step by step. We'll explore definitions of polynomials, including terms like monomials, binomials, and trinomials, while providing clear examples for practice. After understanding FOIL and completing exercises, you’ll have the skills necessary to tackle polynomial multiplication with confidence. Let’s dive into polynomial multiplication and enhance your algebra proficiency!

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Understanding the FOIL Method for Multiplying Binomials

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Presentation Transcript

  1. Warm up What type of equation is this? Find f(2)

  2. FOIL

  3. Definition: Polynomial • An expression containing constants, variables and exponents. • Examples: • Each piece is called a “term”

  4. Special Names • Monomial – Poly with ONE term Ex: • Binomial – Poly with TWO terms Ex: • Trinomial – Poly with THREE terms Ex:

  5. Goal • We can add, subtract, multiply and divide these polynomials. • Today we are going to focus on how to MULTIPLY BINOMIALS.

  6. What is FOIL The FOIL method is ONLY used when you multiply 2 binomials. It is an acronym that tells you which terms to multiply.

  7. FOIL • F - first • O - outside • I - inside • L - last

  8. Example 1 • Use the FOIL method to multiply the following binomials: (y + 3)(y + 7)

  9. (y + 3)(y + 7). F tells you to multiply the FIRST terms of each binomial. y2

  10. (y + 3)(y + 7). O tells you to multiply the OUTER terms of each binomial. y2+7y

  11. (y + 3)(y + 7). I tells you to multiply the INNER terms of each binomial. y2 + 7y +3y

  12. (y + 3)(y + 7). L tells you to multiply the LAST terms of each binomial. y2 + 7y + 3y + 21 Combine like terms. y2 + 10y + 21

  13. Example 2

  14. Example 3 • (2a – 3b)(2a + 4b) • Answer: 4a2 + 2ab – 12b2

  15. Example 4: You try • (y + 4)(y – 3) • Answer:

  16. Example 5: You try • Hint: Remember • Answer:

  17. Example 6: You try • Answer:

  18. Homework • FOIL Puzzle

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