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Multiplication of Polynomials: Binomials, Trinomials, and Binomial Square

This chapter section covers the multiplication of polynomials, including multiplying monomials by polynomials, binomials by polynomials, binomials by binomials, and binomial square. Learn the concepts and techniques through the distributive property, FOIL method, area model, and rule of squares. Practice problems and examples are provided.

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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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