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Math Help - polynomial algebra

  1. #1
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    polynomial algebra

    the polynomial (x+y)^9 is exapned and written out in decreasing powers of x. The second and third terms have equal values when evaluated for x = p and y = q, where p and q are positive integers and p + q = 1. What is the value of p. Use algebra

    so i have:
    9 x^8 y^1 and 36 x^7 y^2 as the two terms...
    and p = q -1

    so
    9 (1-q)^8 q = 36 (1-q)^7 q^2
    and using algebra i dont know how to solve this...from my calc i kno the answer is p = .8 ...but i need to figure it out with algebra
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  2. #2
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    Hello,

    9 (1-q)^8 q = 36 (1-q)^7 q^2
    This is correct

    Now, divide both sides by (1-q)^7 and by 9q.

    I explain why :
    this is equivalent to :

    (9(1-q)^8 q)-(36(1-q)^7 q^2)=0

    Factor out the common factors (q^2=q*q, 36=4*9, (1-q)^8=(1-q)^7*q)

    Then, solve
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