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Mastering the Distributive Property and FOIL Method for Multiplying Binomials

This comprehensive guide covers the Distributive Property and the FOIL method, essential tools for multiplying binomials in algebra. Learn how to multiply each term effectively by applying the outside number to all inside terms while respecting integer rules. With clear examples, such as simplifying 4(5 + x) and multiplying (2x + 3)(5x + 8), students will build confidence in algebraic manipulation. Additional extensions include visual aids like box plots for multiplying polynomials and strategies for overcoming common learning obstacles.

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Mastering the Distributive Property and FOIL Method for Multiplying Binomials

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  1. Warm UpCompute the following equations:4

  2. Distributive Property 1) MULTIPLY the outside # by all inside #s ALWAYS Take the sign IN FRONT! - REMEMBER YOUR MULTIPLYING INTEGER RULES

  3. Examples: Simplify Multiply BOTH inside numbers by the outside number! 4(5 + x) Re-write so the variable term is first!

  4. Multiplying Binomials Multiply. (2x + 3)(5x + 8) Using the distributive property, multiply 2x(5x + 8) + 3(5x + 8). 10x2 + 16x + 15x + 24 Combine like terms. 10x2 + 31x + 24 A shortcut of the distributive property is called the FOIL method.

  5. FOILis an acronym and tells you which terms to multiply. First terms Outer terms Inner terms Last terms http://youtu.be/4Z9grM2SiJw

  6. The FOIL method is ONLY used when you multiply 2 binomials.Use the FOIL method to multiply the following binomials:(y + 3)(y + 7).

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

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

  9. Limitation • If the students are not understanding the concept. • What I have learned: • I still have a lot to learn about teaching • Not every student will understand every concept right away. • Distributing is something students struggle with. • Student want to be able to apply what they learned in elementary school to what they will be learning in high school

  10. Extension • Show the students how to multiply binomials and trinomials using the boxplot. • Factoring using X marks the spot.

  11. Any Questions

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