math

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How do i factor?
a)5a^2b+ab^2
b)9k^2-1
c)2y^2-5y+2
If i can get an idea how to do these and i work the rest i have to do myself, thanks

  • math -

    The first is a simple case of "common factoring"
    5a^2b+ab^2
    = ab(5a+b)
    these can be quickly verified by merely expanding your answers.

    the second is a "difference of squares"
    9k^2-1
    = (3k+1)(3k-1)

    the third is a standard "quadratic trinomial factoring"
    the most popular method these days seems to be "decomposition"
    2y^2-5y+2
    multiply the coefficients of the first and last terms ... 2x2 = 4
    now find two numbers so that when multiplied will give you 4, and when added will give you the coefficient of the middle term, namely -5
    those 2 numbers clearly are -4 and -1

    so rewrite the middle term of -5y as
    -4y -y , thus the name "decomposition"

    = 2y^2 - 4y - y + 2

    now factor by finding the highest common factor of the first two terms

    = 2y(y - 2) - y + 2

    If you did everything correctly, that common factor of y-2 MUST also appear at the end, and surely ....

    = 2y(y-2) - (y-2)

    and a common factor once more ....

    = (y-2)(2y-1)

    again you can always check your answer by expanding it, you must get the original question.

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