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Special Products. MATH 018 Combined Algebra S. Rook. Overview. Section 5.6 in the textbook Multiplying binomials Squaring a binomial Multiplying by the sum and difference of two terms. Multiplying Binomials. Multiplying Binomials.

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  1. Special Products MATH 018 Combined Algebra S. Rook

  2. Overview • Section 5.6 in the textbook • Multiplying binomials • Squaring a binomial • Multiplying by the sum and difference of two terms

  3. Multiplying Binomials

  4. Multiplying Binomials Recall that to multiply two polynomials we use the distributive property: Ensure that each term of one polynomial is multiplied by all the terms of the second polynomial An acronym exists to help us multiply when BOTH polynomials are BINOMIALS Recall the acronym? How many terms does a binomial have? 4

  5. FOIL FOIL is essentially using the Distributive Property: To use FOIL on (x + 1)(x + 2): First (x + 1)(x + 2) = x2 Outer (x + 1)(x + 2) = 2x Inner (x + 1)(x + 2) = x Last (x + 1)(x + 2) = 2 Combine like terms Verify to yourself that the result is the same when using the Distributive Property 5

  6. Multiplying Binomials (Example) Ex 1: Multiply using FOIL and then verify to yourself that the result is the same when using the Distributive property: a) (x + 2)(x – 5) b) (3x – 1)(4x + 7)

  7. Squaring Binomials

  8. Squaring Binomials How would we expand the monomial x2? How would we expand (a + b)2? After expanding, how would we finish the multiplication? ALWAYS expand a squared binomial BEFORE multiplying! Do NOT just square each of the individual terms! (a + b)2 ≠a2 + b2 (3 + 4)2 ≠ 32 + 42 8

  9. Squaring Binomials (Example) Ex 2: Simplify: a) (x + 5)2 b) (2x – 7)2 c) (3r + 4s)2

  10. Multiplying by the Sum and Difference of Two Terms

  11. Multiplying by the Sum and Difference of Two Terms A pair of binomials where the two terms are the same but with different signs: (a + b)(a – b) Observe what happens to the middle terms when multiplying two such binomials e.g. Multiply (x – 1)(x + 1) 11

  12. Multiplying by the Sum and Difference of Two Terms (Example) Ex 3: Simplify: a) (x + 8)(x – 8) b) (6x + 5y)(6x – 5y)

  13. Summary • After studying these slides, you should know how to do the following: • Multiplying binomials • Squaring binomials • Multiplying by the sum and difference of two terms • Additional Practice • See the list of suggested problems for 5.6 • Next lesson • Dividing Polynomials (Section 5.7)

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