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Transcript
Math 90 4.6 "Multiplying Polynomials" Objectives: * Multiply polynomials. * Find special products. * Use multiplication to simplify expressions. Multiplying Monomials Multiplying Monomials: kTo multiply two monomials, multiply the numerical factors (the coe¢ cients) and then multiply the variable factors.k Example 1: (Multiplying monomials) Multiply the following monomials. a) 2y 3 4y 2 b) 5ab3 c ( 3abc) 6a2 b2 c2 Multiply a Polynomial by a Monomial Multiplying Polynomials by Monomials kTo multiply a monomial and a polynomial, multiply each term of the polynomial by the monomial.k Example 2: (Multiplying a polynomial by a monomial) Multiply the following expressions. a) 3x2 5x6 + 4x2 b) 2ab2 3a3 b 2a2 b + 4b2 Multiply Two Binomials Example 3: (Multiplying two binomials) Multiply the following binomials. a) (3x + 4) (2x 9) b) Page: 1 5y 2 4 1 + 2y 2 Notes by Bibiana Lopez Beginning and Intermediate Algebra by Gustafson and Frisk 4.6 The FOIL Method The FOIL Method: To multiply two binomials, A + B and C + D : Step 1: Multiply First terms: Step 2: Multiply Outside terms: =) (A + B) (C + D) = Step 3: Multiply Inside terms: Step 4: Multiply Last terms: Example 4: (Using the FOIL method) Multiply the following polynomials: a) (x + 4) (x c) (1 + 2x) (1 4) 3x) b) d) 2x2 w+ 3 3 4 x3 w+ 2 3 4 Special Products: 2 (x + y) = (x 2 y) = (x + y) (x y) = Page: 2 Notes by Bibiana Lopez Beginning and Intermediate Algebra by Gustafson and Frisk 4.6 Example 5: (Special products) Find each product: a) (2a 2 2 3b) d) (x + 2y) c) (4x + 5y) (4x 5y) Multiply Any Two Polynomials Multiplying Polynomials To multiply two polynomials, multiply each term of one polynomial by each term of the other polynomial, and then combine like terms. Example 6: (Multiplying polynomials) Multiply the following polynomials. a) 3y 2 + y 4y 2 b) (2a + b) 3a2 2y + 5 4ab b2 Multiply Three Polynomials Example 7: (Multiplying three polynomials) Multiply the following polynomials. a) 2r (r 2s) (5r 4s) b) (2x Page: 3 3 y) Notes by Bibiana Lopez Beginning and Intermediate Algebra by Gustafson and Frisk 4.6 Multiply Binomials to Solve Equation Example 8: (Solve equations) Solve: a) (y 5) (y 2) = y 2 4 b) (x + 2) (x Page: 4 4) = (x + 6) (x 3) Notes by Bibiana Lopez