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Multiplication of Polynomials: Binomials, Trinomials, and Binomial Square

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  1. Chapter 5 Section 2 Multiplication of Polynomials

  2. Monomial and Polynomial • Use the distributive property

  3. Binomial and Trinomial • Distribute the binomial’s terms

  4. Binomial and Polynomial • Distribute the terms of the binomial

  5. Two Binomial • Two ways • Foil • Area model

  6. Two Binomial • Foil • (3x + 5y)(x – 2y) • F – Front – two front terms in each binomial: (3x)(x) • O – Outside – two outside terms: (3x)(-2y) • I – Inside – two inside terms: (5y)(x) • L – Last – two last terms: (5y)(-2y)

  7. Two Binomial • Multiply • (x + 3)(x + 2) • (2x – 3)(5x – 4)

  8. Two Binomial • (3x + 5y)(x – 2y) • Area Model 3x 5y • Find the area of x each region -2y

  9. Show on paper • (3x + 5y)(x – 2y) Area model

  10. Two Binomial • Multiply • (x + 3)(x + 2) • (2x – 3)(5x – 4)

  11. Binomial Square • Square of a binomial • Way 1 • Use area model • Use rule • Meaning of the exponent

  12. Use paper • Show area model • Show rule • Explain rule • (fist term)2 +- 2(first)(last) + (last)2

  13. Sum, Difference of Two Terms • (A + B)(A – B) • Area model • Rule • A2 – B2 • (9x + 5)(9x - 5)

  14. Simplify 1) 2) 3) 4) (5x – 3)(5x + 3) 5)

  15. Multiplication of Polynomial Functions • (fg)(x) = f(x) • g(x) • If f(x) = x – 5 and g(x) = x – 2 find • (fg)(x) • (gf)(3)

  16. Practice Find the product • 3x2(3x + 2) • (x – 1)(x2 + x + 2) • (3x – 2y)(2x – 5y) • (3x – 4y)2 • (8x – 7y)(8x + 7y)

  17. Summary • Multiplied the following • Monomial by Polynomial • Binomial by Polynomial • Binomial by Binomial • Binomial Square • Sum, Difference of Two Binomials • Multiply Polynomial Functions

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