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The question is: Find the indicated product

  1. Sep 27, 2015 #1
    So basicly our teacher taught us in high school how to find the product of some equations but I do not understand it very well and I need someone to teach me how to solve this basic problem.

    The Equation is : (3x^2-4x+1)(4x^2+x-2)

    I do not know how to find the product of that problem can anyone please help me with it?
     
  2. jcsd
  3. Sep 27, 2015 #2

    Mentallic

    User Avatar
    Homework Helper

    For every term in the first factor, multiply it by the entire second factor. For example,

    [tex](a+b)(c+d)=a(c+d) + b(c+d)[/tex]
     
  4. Sep 27, 2015 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    You do the same thing with polynomials that you do with numbers. If you were asked to multiply 233 by 123, you would first multiply 233 by the first digit in 123, 3
    699. Then multiply by 2: 466. Finally multiply by 1: 233

    You would position those as
    ___233
    __x123
    ______
    __699
    _466
    233
    ______
    28659

    That spacing is because 123= 100+ 20+ 3 so you are actually multiplying (100+ 20+ 3)233= 100(233)+ 20(233)+ 3(233) (that's the "distributive law").

    Similarly to multiply (3x^2-4x+1)(4x^2+x-2) think of it as 3x^2(4x^2+ x- 2)- 4x(4x^2+ x- 2)+ 1(4x^2+ x- 2). You can do each of those by using the "distributive law" again:
    3x^2(4x^2+ x- 2)= (3x^2)(4x^2)+ (3x^2)(x)+ (3x^2)(-2)= 12x^4+ 3x^3- 6x^2.
    -4x(4x^2+ x- 2)= (-4x)(4x^2)+ (-4x)(x)+ (-4x)(-2)= -16x^3- 4x^2+ 8x
    1(4x^2+ x- 2)= (1)(4x^2)+ (1)(x)+ 1(-2)= 4x^2+ x- 2.

    Now add those combining "like terms" (terms with the same power of x). The only "x^4" term is 12x^4. The "x^3" terms are 3x^3 and -16x^3- their sum is -13x^3. The "x^2" terms are -6x^2, -4x^2, and 4x^2. They add to -6x^2. The "x" terms are 8x and x. They add to 9x. Finally, the only "constant term" is "-2". That is, the product is 12x^4- 13x^3- 6x^2+ 9x- 2.

    In a nutshell, multiply each term in one polynomial by each term in the other, then "combine like terms".
     
  5. Sep 27, 2015 #4
    But what do I do with the exponents? do I add them up?
    For exemple (3x^2)(4x^2) = 12x^4
    like ^2+^2?
     
  6. Sep 27, 2015 #5

    Ssnow

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    Gold Member

    yes, using power properties in the same bases ## a^{n}\cdot a^{ m}=a^{n+m}##, remember if ##a\not=0 \Rightarrow a^{0}=1## ...
     
  7. Sep 27, 2015 #6

    Mark44

    Staff: Mentor

    Let's get some terminology down. The above is a product, but it is not an equation -- this is an algebraic expression. An equation has = in it, and states that two expressions have the same value. The expressions above are made up of three terms each. The terms are the things being added or subtracted.

    To expand (multiply out) the expression above, you need to multiply each term in the second expression by each term in the first expression. All together you will have nine multiplications. Some of these intermediate multiplications will have terms that have the same variable part (such as x3) but different coefficients (the constant that multiplies the variable part). These are called like terms, and can be combined. For example, two of the multiplications are 3x2 times x and -4x times 4x2. The first product gives 3x3 and the second product gives -16x3. We can combine 3x3 - 16x3 to -13x3, using the distributive property -- am + bm = (a + b)m.

    You said that you had studied this in high school. If you are studying this material again, are you working from a textbook? If not, it would be useful to get an algebra textbook, which would list all of the various properties you need to use to carry out the multiplication you're interested in.
     
  8. Sep 27, 2015 #7
    Alright thanks I`ll try buying a good Algebra textbook and hopefully it can help me even more thanks for all the help guys!
     
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