Results 1 to 3 of 3

Math Help - Problems to Check

  1. #1
    Newbie
    Joined
    Nov 2007
    Posts
    9

    Problems to Check

    Some more problems I would like checked please. Numbers in red are exponents. My answers are in bold.

    Problem 1: (Simplify)

    (4a2) (5a)

    = 42(a2) * 5(a)

    = 4a2 * 5a

    = 4 * 5 * a2 * a

    = 20a2

    ________

    Problem 2: (Simplify)

    (-3xy) (4x2y3)

    = -3 (x)(y) * 4 (x2)(y3)

    = -3xy * 4x2y3

    = -3 * 4 * x * x2 *y * y3

    = -12x2y3

    __________

    Problem 3: (Simplify)

    (-3x3y2)(5x5y)

    = -3(x3)(y2) * 5(x5)(y)

    = -3x3y2 * 5x5y

    = -3 * 5 * x3 * x5 * y2 * y

    = -15x15y2

    __________

    Problem 4: (Simplify)

    (-3ab2c3)(-5ac)

    = -3(a)(b2)(c3) * -5(a)(c)

    = -3ab2c3 * -5ac

    = -3 * -5 * a * b2 * c3 *c

    = 15ab2c3


    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,802
    Thanks
    692
    Hello, slykksta!

    You're forgetting that: . x \:=\:x^1



    1)\;(4a^2)(5a)
    We have: . (4\cdot a^2)\cdot(5\cdot a) \;=\;(4\cdot5)\cdot(a^2\cdot a^{{\color{red}1}}) \:=\:20\,a^{{\color{red}3}}


    2) \;(\text{-}3xy) (4x^2y^3)
    We have: . (\text{-}3\cdot x\cdot y)\cdot(4\cdot x^2\cdot y^3) \;=\;(\text{-}3)(4)\cdot (x^{{\color{red}1}}\cdot x^2)\cdot(y^{{\color{red}1}}\cdot y^3) \;=\;-12\,x^{{\color{red}3}}\,y^{{\color{red}4}}


    3)\;(\text{-}3x^3y^2)(5x^5y)
    We have: . (\text{-}3\cdot x^3\cdot y^2)\cdot (5\cdot x^5\cdot y) \;=\;(\text{-}3)(5)\cdot(x^3\cdot x^5)\cdot(y^2\cdot y^{{\color{red}1}}) \;=\;-15\,x^{{\color{red}8}}\,y^{{\color{red}3}}


    4)\;(\text{-}3ab^2c^3)(\text{-}5ac)
    We have: . (\text{-}3\cdot a\cdot b^2\cdot c^3)\cdot(\text{-}5\cdot a\cdot c) \;=\;(\text{-}3)(\text{-}5)\cdot(a^{{\color{red}1}}\cdot a^{{\color{red}1}})\cdot (b^2)\cdot(c^3\cdot c^{{\color{red}1}}) \;=\;15\,a^{{\color{red}2}}\,b^2\,c^{{\color{red}4  }}

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,054
    Thanks
    368
    Awards
    1
    Quote Originally Posted by slykksta View Post
    Some more problems I would like checked please. Numbers in red are exponents. My answers are in bold.

    Problem 1: (Simplify)

    (4a2) (5a)

    = 42(a2) * 5(a)

    = 4a2 * 5a

    = 4 * 5 * a2 * a

    = 20a2

    ________
    Several of your steps here don't make sense.
    (4a^2)(5a) = (4 \cdot 5)(a^2 \cdot a) = 20a^{2 + 1} = 20a^3

    Quote Originally Posted by slykksta View Post
    Problem 2: (Simplify)

    (-3xy) (4x2y3)

    = -3 (x)(y) * 4 (x2)(y3)

    = -3xy * 4x2y3

    = -3 * 4 * x * x2 *y * y3

    = -12x2y3

    __________
    I'm seeing a pattern here. Recall the rule for addition of exponents:
    a^n \cdot a^m = a^{n + m}

    So x \cdot x^2 = x^1 \cdot x^2 = x^{1 + 2} = x^3.

    Try this one again.

    Quote Originally Posted by slykksta View Post
    Problem 3: (Simplify)

    (-3x3y2)(5x5y)

    = -3(x3)(y2) * 5(x5)(y)

    = -3x3y2 * 5x5y

    = -3 * 5 * x3 * x5 * y2 * y

    = -15x15y2

    __________
    Ah! I see. You are multiplying the exponents.
    x^3 \cdot x^5 \neq x^{15}

    x^3 \cdot x^5 = x^{3 + 5} = x^8

    You multiply exponents in this situation:
    (a^n)^m = a^{nm}

    Quote Originally Posted by slykksta View Post
    Problem 4: (Simplify)

    (-3ab2c3)(-5ac)

    = -3(a)(b2)(c3) * -5(a)(c)

    = -3ab2c3 * -5ac

    = -3 * -5 * a * b2 * c3 *c

    = 15ab2c3
    Same problems as I mentioned above.

    -Dan
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Could someone check a few problems for me?
    Posted in the Statistics Forum
    Replies: 2
    Last Post: July 18th 2010, 08:55 PM
  2. Could someone check my problems for me?
    Posted in the Statistics Forum
    Replies: 2
    Last Post: July 18th 2010, 11:50 AM
  3. Replies: 3
    Last Post: October 15th 2009, 04:18 AM
  4. Please check my problems again..
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: July 16th 2009, 11:33 AM
  5. Algebra 2 problems...check work
    Posted in the Algebra Forum
    Replies: 2
    Last Post: December 2nd 2007, 07:07 PM

Search Tags


/mathhelpforum @mathhelpforum