Algebra

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I need to use Pascal's Triangle to expand (x-1)^5

I know I use the fifth row but I'm not sure how to do it- I have a bunch of these and I'm really confused- Please help if you can-

  • Algebra -

    you know the expansion must look like
    ?x^5(-1)^0 + ?x^4(-1)^1 + ?x^3(-1)^2 + ?x^2(-1)^3 + ?x^1(-1)^4 + ?x^0(-1)^5
    = ?x^5 - ?x^4 + ?x^3 - ?x^2 + ?x - ?

    now the 5th row of the triangle has values:
    1 5 10 10 5 1
    put these in where the ?'s are and you are done

    = x^5 - 5x^4 + 10x^3 - 10x^2 + 5x - 1

    suppose you had
    (x+2)^4
    = 1x^4 + 4x^3(2) + 6x^2(2^2) + 4x(2^3) + 12^4
    = x^4 + 8x^3 + 24x^2 + 32x + 16

  • Algebra -

    That last term in the 2nd last row of course is 1(2^4) or 16

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