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Easy

Question

How is ( x + y )n obtained from (x + y)n-1

hintHint:

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 ≥ 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 from left parenthesis x plus y right parenthesis to the power of n minus 1 end exponent .

The correct answer is: = 1736



    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 ( x + y ) , that is:

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 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 end cell row cell 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 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 end cell row cell 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 end cell row cell 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 end cell row cell 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 end cell end table
     

    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 (  x + y)  with left parenthesis x plus y right parenthesis to the power of n minus 1 end exponent .

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