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Easy

Question

How is left parenthesis x plus y right parenthesis to the power of n obtained from left parenthesis x plus y right parenthesis to the power of n minus 1 end exponent

The correct answer is: You could also get the value of from by just multiplying a with .


    ANSWER:
    Hint:
    left parenthesis x plus y right parenthesis to the power of n equals to the power of n C subscript 0 x to the power of n y to the power of 0 plus to the power of n C subscript 1 x to the power of n minus 1 end exponent y to the power of 1 plus to the power of n C subscript 2 x to the power of n minus 2 end exponent y squared plus horizontal ellipsis plus to the power of n C subscript n minus 1 end subscript x to the power of 1 y to the power of n minus 1 end exponent plus to the power of n C subscript n x to the power of 0 y to the power of n, where  n greater or equal than 0 is called the binomial expansion of left parenthesis x plus y right parenthesis to the power of n.
    We are asked to find how left parenthesis x plus y right parenthesis to the power of n can be obtained fromleft parenthesis x plus y right parenthesis to the power of n minus 1 end exponent .
    Step 1 of 1:
    The binomial expansion of
    left parenthesis x plus y right parenthesis to the power of n minus 1 end exponent equals to the power of n minus 1 end exponent C subscript 0 x to the power of n minus 1 end exponent y to the power of 0 plus to the power of n minus 1 end exponent C subscript 1 x to the power of n minus 2 end exponent y to the power of 1 plus to the power of n minus 1 end exponent C subscript 2 x to the power of n minus 3 end exponent y squared plus horizontal ellipsis plus to the power of n minus 1 end exponent C subscript n minus 2 end subscript x to the power of 1 y to the power of n minus 2 end exponent plus to the power of n minus 1 end exponent C subscript n minus 1 end subscript x to the power of 0 y to the power of n minus 1 end exponent
    Multiply then expansion by left parenthesis x plus y right parenthesis , that is:
    left parenthesis x plus y right parenthesis to the power of n minus 1 end exponent left parenthesis x plus y right parenthesis equals left parenthesis x plus y right parenthesis open parentheses blank to the power of n minus 1 end exponent C subscript 0 x to the power of n minus 1 end exponent y to the power of 0 plus to the power of n minus 1 end exponent C subscript 1 x to the power of n minus 2 end exponent y to the power of 1 plus to the power of n minus 1 end exponent C subscript 2 x to the power of n minus 3 end exponent y squared plus horizontal ellipsis plus to the power of n minus 1 end exponent C subscript n minus 2 end subscript x to the power of 1 y to the power of n minus 2 end exponent plus to the power of n minus 1 end exponent C subscript n minus 1 end subscript x to the power of 0 y to the power of n minus 1 end exponent close parentheses
    left parenthesis x plus y right parenthesis to the power of n minus 1 plus 1 end exponent equals x open parentheses blank to the power of n minus 1 end exponent C subscript 0 x to the power of n minus 1 end exponent y to the power of 0 plus to the power of n minus 1 end exponent C subscript 1 x to the power of n minus 2 end exponent y to the power of 1 plus to the power of n minus 1 end exponent C subscript 2 x to the power of n minus 3 end exponent y squared plus horizontal ellipsis plus plus to the power of n minus 1 end exponent C subscript n minus 2 end subscript x to the power of 1 y to the power of n minus 2 end exponent plus to the power of n minus 1 end exponent C subscript n minus 1 end subscript x to the power of 0 y to the power of n minus 1 end exponent close parentheses
    plus y open parentheses blank to the power of n minus 1 end exponent C subscript 0 x to the power of n minus 1 end exponent y to the power of 0 plus to the power of n minus 1 end exponent C subscript 1 x to the power of n minus 2 end exponent y to the power of 1 plus to the power of n minus 1 end exponent C subscript 2 x to the power of n minus 3 end exponent y squared plus horizontal ellipsis plus to the power of n minus 1 end exponent C subscript n minus 2 end subscript x to the power of 1 y to the power of n minus 2 end exponent plus to the power of n minus 1 end exponent C subscript n minus 1 end subscript x to the power of 0 y to the power of n minus 1 end exponent close parentheses
    left parenthesis x plus y right parenthesis to the power of n equals open parentheses blank to the power of n minus 1 end exponent C subscript 0 x to the power of n y to the power of 0 plus to the power of n minus 1 end exponent C subscript 1 x to the power of n minus 1 end exponent y to the power of 1 plus to the power of n minus 1 end exponent C subscript 2 x to the power of n minus 2 end exponent y squared plus horizontal ellipsis plus to the power of n minus 1 end exponent C subscript n minus 2 end subscript x squared y to the power of n minus 2 end exponent plus to the power of n minus 1 end exponent C subscript n minus 1 end subscript x to the power of 1 y to the power of n minus 1 end exponent close parentheses plus
    open parentheses blank to the power of n minus 1 end exponent C subscript 0 x to the power of n minus 1 end exponent y to the power of 1 plus to the power of n minus 1 end exponent C subscript 1 x to the power of n minus 2 end exponent y squared plus to the power of n minus 1 end exponent C subscript 2 x to the power of n minus 3 end exponent y cubed plus horizontal ellipsis plus to the power of n minus 1 end exponent C subscript n minus 2 end subscript x to the power of 1 y to the power of n minus 1 end exponent plus to the power of n minus 1 end exponent C subscript n minus 1 end subscript x to the power of 0 y to the power of n close parentheses
    Note:
    You could also get the value of left parenthesis x plus y right parenthesis to the power of n from left parenthesis x plus y right parenthesis to the power of n minus 1 end exponent by just multiplying a left parenthesis x plus y right parenthesis with left parenthesis x plus y right parenthesis to the power of n minus 1 end exponent .

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