Ch Part 1 Multiplying Polynomials

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Presentation transcript:

Ch. 12-4 Part 1 Multiplying Polynomials ~Multiply Coefficients and add exponents of like bases. Example 1: Multiply the following monomials. a.) (4a3)(-5a2) b.) (2y4)(4y) -20a5 8y5 Example 2: Multiply the following monomials. a.) (-3x3)(2x5) b.) (x2)(16x) -6x8 16x3

We know that 5(3 + 4) = 5(3) + 5(4) = 15 + 20 = 35 Now that you can multiply monomials, you can put the distributive property to work. We know that 5(3 + 4) = 5(3) + 5(4) = 15 + 20 = 35 In the same way 5(3x + 4y) = 5(3x) + 5(4y) = 15x + 20y Example 3: Multiply each monomial by each binomial. a.) 3x(2x + 8) b.) 2x(x + 4y) c.) –y2(2y + 7) d.) -2d3(d2 – 1) 6x2 + 24x 2x2 + 8xy -2y3 – 7y2 -2d5 + 2d3

Ch. 12-4 Part 2 Multiplying Polynomials You have learned to use the distributive axiom to multiply a polynomial by a monomial: (4x + 3)(3x) = 12x2 + 9x If you replace 3x in the example above by the polynomial 3x + 4, the distributive axiom can still be applied: (4x+ 3)(3x + 4) An easy way to multiply polynomials is called using the FOIL method. FOIL First Outer Inner Last

FOIL OR Box Method First Outer Inner Last (4x + 3)(3x + 4) 4x 3 3x 4 First: 4x(3x) = 12x2 (4x + 3)(3x + 4) Outer: 4x(4) = 16x Inner Outer Inner: 3(3x) = 9x Last: 3(4) = 12 OR Then rewrite the problem: Box Method 12x2 + 9x + 16x + 12 4x 3 3x 4 Then simplify any like terms 12x2 + 25x + 12 12x2 9x 16x 12

Example 1: Multiply the following binomials. a.) (2x + 1)(3x + 2) b.) (x + 1)(2x + 5) c.) (3x + 4)(2x – 1) d.) (2x – 2)(x – 3) 6x2 + 7x + 2 2x2 + 7x + 5 6x2 + 5x - 4 2x2 – 8x + 6