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Mastering Binomial Multiplication: FOIL Method Explained

This guide provides a step-by-step approach to multiplying binomials using the FOIL method—First, Outer, Inner, Last. By breaking down expressions like (x+5)(x+8) and others, we demonstrate how to apply distribution effectively. We illustrate combining like terms with examples, including quadratic expressions and their coefficients. The process is made clear with practical exercises, such as multiplying (3x+2)(x+5) and (5x²-2x)(x-7). Mastering this technique is essential for success in algebra. Ready to practice on your own? Refer to your homework page 242 (22-34).

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Mastering Binomial Multiplication: FOIL Method Explained

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  1. 5.9 Continued…. Multiplying a Binomial by a Binomial

  2. Steps: • Distribute the 1st term • Distribute the 2nd term • Add like terms Ex: (x+5) (x+8)

  3. “F O I L” Multiplication • F irst • O uter • I nner • L ast (x + 2) (x + 3) x2 + 3x + 2x + 6 x2 + 5x + 6

  4. Use FOIL to multiply (3x + 2)(x + 5) 3x2 + 15x + 2x + 10 3x2 + 17x + 10

  5. Use FOIL to multiply (2x2 - 1)(x - 3) 2x3 - 6x2 - x1 + 3 2x3 - 6x2 – x + 3

  6. Use FOIL to multiply (5x2 – 2x)(x - 7) + 14x1 5x3 - 35x2 -2x 2 5x3 - 37x2 + 14x

  7. Use FOIL to multiply (1 - 2x2) (1 + 3x) 1 + 3x1 -2x2 + 6x3 6x3 - 2x2 + 3x+ 1

  8. Use FOIL to multiply (1 - 2x2) (1 + 3x) 1 + 3x1 -2x2 - 6x3 -6x3 - 2x2 + 3x+ 1

  9. Use FOIL to multiply (4xy - y2) (xy + y2) 4x2y2 + 4xy3 -xy 3 - y4 4x2y2 + 3xy3 – y4

  10. Homework Page 242 (22-34) all

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