Transcript Slide 1
Multiplying Polynomials MATH 018 Combined Algebra S. Rook Overview • Section 5.5 in the textbook: – Multiplying monomials – Multiplying monomials by polynomials – Multiplying two polynomials – Multiplying polynomials vertically 2 Multiplying Monomials 3 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? 4 Multiplying Monomials (Example) Ex 1: Simplify: a) 9a2b · 8a5 b) -x3yz4 · 2y2z 5 Multiplying Monomials by Polynomials 6 Multiplying Monomials by Polynomials • Use the distributive property • Simplify using exponent rules 7 Multiplying Monomials by Polynomials (Example) Ex 2: Simplify: a) 5x(x2 – 5x + 6) b) -2y(8y2 – 3y – 1) 8 Multiplying Two Polynomials 9 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 10 distributive property more evident? 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 Multiplying Polynomials Vertically 12 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 13 Multiplying Polynomials Vertically (Example) Ex 4: Multiply vertically: a) (3x2 + x – 5)(x + 3) b) (10x2 – 4x + 1)(x – 2) 14 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) 15