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Multiplying Polynomials

Multiplying Polynomials. Distribute and FOIL. Monomial ∙ Monomial. No distribution here – everything is already just multiply! You multiply number with numbers You multiply variables with same variables adding exponents.

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Multiplying Polynomials

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  1. MultiplyingPolynomials Distribute and FOIL

  2. Monomial ∙ Monomial No distribution here – everything is already just multiply! You multiply number with numbers You multiply variables with same variables adding exponents Remember: You can multiply any monomial with another – they do not need to be like terms!

  3. Monomial ∙ Binomial Distribute multiplication over addition or subtraction You multiply number with numbers You multiply variables with same variables adding exponents

  4. Binomial ∙ Binomial Multiplying a binomial by another binomial requires more than one distributing step. Multiply: (2x + 7)(3x + 5) Distribute 2x(3x + 5) and distribute 7(3x + 5): 6x2+ 10x 21x + 35 Then add those products, adding like terms: = 6x2+ 31x + 35 6x2+ 10x+ 21x + 35

  5. (2x + -3)(4x + 5) = 8x2 + 10x + -12x + -15 = 8x2 + -2x + -15 F.O.I.L. There is an acronym to help us remember how to multiply two binomials. (2x + -3)(4x + 5) F : Multiply the First term in each binomial. 2x • 4x = 8x2 O : Multiply the Outer terms in the binomials. 2x • 5 = 10x I : Multiply the Inner terms in the binomials. -3 • 4x = -12x L : Multiply the Last term in each binomial. -3 • 5 = -15

  6. F.O.I.L. Use the FOIL method to multiply these binomials: 1) (3x + 4)(2x + 1) 2) (x + 4)(x - 5) 3) (x + 5)(x - 5) 4) (4c - 3)(2c - 5) 5) (2w + 3)(2w - 3)

  7. Homework Pg. 176 #2 to 34 even

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