Anonymous
Anonymous asked in Science & MathematicsMathematics · 3 months ago

How do you factor a trinomial? ?

20a²b - 25ab + 45ab²

16 Answers

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  • 3 months ago

    5ab (4a - 5 + 9b)

    Source(s): Math
  • 3 months ago

    Factor out 5ab.

    Divide each term by 5ab.

    20a²b - 25ab + 45ab²

    Answer: 5ab(4a - 5 + 9b)

    You can also write the answer as

    5ab(4a + 9b - 5)

    Either one is acceptable. 

  • 3 months ago

    20a²b - 25ab + 45ab²

    = 5ab(4a - 5 + 9b)  Answer//

  • garry
    Lv 4
    3 months ago

    sorry forgot my algebra after 60 years , as a professer.

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  • Amy
    Lv 7
    3 months ago

    Use the Distributive Property to remove any factor common to all terms.

    14x²z + 28xyz + 35xz = 7xz(2x + 4y + 5)

    That's all that can be done to the example you gave. 

    But if you end up with powers of variables in the form {x^2, xy, y^2}, it is sometimes possible to factor it further. This form includes {x^2, x, 1} and higher powers such as {x^6, x^3 y, y^2}

    You can use the Quadratic Formula, use logic to guess at likely factors and check whether they divide the trinomial, or guess-and-check how to split the middle term in order to use the distributive property again.

    4x^2 - 5x - 9 = 4x^2 + 4x - 9x - 9 = (x+1)(4x - 9)

  • sepia
    Lv 7
    3 months ago

    20a²b - 25ab + 45ab²

    = 20a²b + 45ab² - 25ab

    = 5ab(4a + 9b - 5)

  • 3 months ago

    20a²b - 25ab + 45ab²

    = 5ab(4a + 9b - 5)

  • David
    Lv 7
    3 months ago

    It is: 5ab(4a -5 +9b) when factored

  • david
    Lv 7
    3 months ago

    There are different kinds of trinomials.  You should be learning some patterns which will allow you to know which kind of trinomial this is and what kind of factoring to use.   1st 'rule' of factoring is to look for a greatest common factor.  Look at the coefficients .. is there a common factor?  20,  25, and 45  are all multiples of 5 .. 5 is their GCF.

     .. next look at the variables from each term

      a^2b,  ab,  ab^2  <<<<  each have both an a and b  ... so the GCF for the variables is  ab

      20a^2b - 25ab + 45ab^2

    = (5ab)(4a)  -  (5ab)(5)   +  (5ab)(9b)

    =  (5ab)(4a - 5 + 9b)  >> answer

  • Ian H
    Lv 7
    3 months ago

    In this example just find the most that all 3 terms have in common.

    20a^2b - 25ab + 45ab^2

    They all have at least one a.

    They all have at least one b.

    The highest common factor of 20, 25 and 45 is just 5.

    If you divide 20a^2b - 25ab + 45ab^2 by 5ab

    you get 4a – 5 + 9b so you now know that

    20a^2b - 25ab + 45ab^2 = 5ab(4a – 5 + 9b)

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