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Multiplying Polynomials

2. Overview. Section 5.5 in the textbook:Multiplying monomialsMultiplying monomials by polynomialsMultiplying two polynomialsMultiplying polynomials vertically. 3. Multiplying Monomials. . 4. 4. Multiplying Monomials. Simplify using exponent rulesJust like when we worked problems in section 5.1

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Multiplying Polynomials

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    1. Multiplying Polynomials MATH 018 Combined Algebra S. Rook

    2. 2 Overview Section 5.5 in the textbook: Multiplying monomials Multiplying monomials by polynomials Multiplying two polynomials Multiplying polynomials vertically

    3. 3 Multiplying Monomials

    4. 4 Multiplying Monomials Simplify using exponent rules Just like when we worked problems in section 5.1 Which exponent rule is used when the operation is multiplication?

    5. Multiplying Monomials (Example) Ex 1: Simplify: a) 9a2b · 8a5 b) -x3yz4 · 2y2z 5

    6. 6 Multiplying Monomials by Polynomials

    7. 7 Multiplying Monomials by Polynomials Use the distributive property Simplify using exponent rules

    8. Multiplying Monomials by Polynomials (Example) Ex 2: Simplify: a) 5x(x2 – 5x + 6) b) -2y(8y2 – 3y – 1) 8

    9. 9 Multiplying Two Polynomials

    10. 10 Multiplying Two Polynomials To multiply (4x + 3)(2x2 – 3x + 7), we again use the distributive property Need to multiply each term of the first polynomial by the second polynomial Multiplying all possible monomials between the two polynomials Simplify and combine any like terms How could we rewrite the multiplication of the above polynomials to make the distributive property more evident?

    11. Multiplying Two Polynomials (Example) Ex 3: Simplify: a) (x – 3)(x + 5) b) (4 – x)(3x – 2) c) (3x – 2)(4x2 + 2x – 3) d) (x2 + 2x – 2)(x2 – 3x – 1) 11

    12. 12 Multiplying Polynomials Vertically

    13. 13 Multiplying Polynomials Vertically An alternative to multiplying polynomials horizontally Works just like multiplying two numbers e.g. 452 · 12 Line up like terms before multiplying

    14. Multiplying Polynomials Vertically (Example) Ex 4: Multiply vertically: a) (3x2 + x – 5)(x + 3) b) (10x2 – 4x + 1)(x – 2) 14

    15. 15 Summary After studying these slides, you should know how to do the following:s Multiply monomials Multiply by monomials Multiply polynomials horizontally Multiply polynomials vertically Additional Practice See the list of suggested problems for 5.5 Next lesson Special Products (Section 5.6)

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