Algebra 6 Point 1
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Algebra 6 Point 1

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    Algebra 6 Point 1 Algebra 6 Point 1 Presentation Transcript

    • 6.1 Multiplying Monomials
      Objective:
      • To multiply monomials
      Frameworks: 10.P.1, 10.P.7
    • What is 36?
      36 = 3 * 3 * 3 * 3 * 3 * 3
      How else can we look at 36?
      36 = (3 * 3) * (3 * 3 * 3 * 3) =32 * 34
      36 = (3 * 3 * 3) * (3 * 3 * 3) = 33 * 33
      36 = (3 * 3 * 3 * 3 * 3) * 3 = 35 = 31
      What is the pattern?
    • What is a monomial?
      A monomial is either a constant, a variable, or a product of a constant and one or more variables:
      Constants: 1 -3 ⅓ 5.2
      Variables: x k a
      Product: 4x3 -5xy πr2 (⅛)x
      NOT a monomial: a2 + b2
    • Multiplying Monomials
      The monomials a3 and a4 have the same base a but different exponents, 3 and 4.
      To multiply a3 and a4, we add the 3 and the 4:
      a3 * a4 = (a*a*a)*(a*a*a*a) = a3+4 = a7
    • Product of Powers
      For all real numbers b and all positive integers m and n,
      bm * bn = bm+n
    • Try some:
      r7 * r
      c2 * d2
      x4 * y6
      a2 * a3
    • What about (-3c2d)(7cd3)?
      Use the commutative and associative properties of multiplication to group the constant coefficients together and the like bases together:
      (-3*7)*(c2*c)(d*d3)
      -21c3d4
    • Try some:
      (-5x2y)(-xz3)
      x2y(x2y2)
      Evaluate for x = -3 and y = -1
    • Try some:
      (3a5b4c)(-2b3c8)
      (xy3)(x2y3)
      Evaluate for x = -5 and y = 2
    • Turn to page 202
      Do 1-12