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Question

Use binomial theorem to expand expression (x + y)7 .

hintHint:

The binomial expansion is left parenthesis x plus y right parenthesis to the power of n equals sum from k equals 0 to n of   n C subscript k x to the power of n minus k end exponent y to the power of k comma text  here  end text n greater or equal than 0.
We are asked to find the binomial expansion of  ( x + y)7 using binomial theorem.

The correct answer is: n+ 1 term.


     Step 1 of 2:
    The given expression is ( x + y)7 . Here, the value of n=7. Thus, there are 7+1=8 terms in the expansion.
    Step 2 of 2:
    Substitute the values in the expansion to get the terms of the expansion. Thus, we have:

    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 7 equals 7 C subscript 0 x to the power of 7 plus 7 C subscript 1 x to the power of 6 left parenthesis y right parenthesis plus 7 C subscript 2 left parenthesis x right parenthesis to the power of 5 left parenthesis y right parenthesis squared plus 7 C subscript 3 left parenthesis x right parenthesis to the power of 4 left parenthesis y right parenthesis cubed plus 7 C subscript 4 left parenthesis x right parenthesis cubed left parenthesis y right parenthesis to the power of 4 plus 7 C subscript 5 left parenthesis x right parenthesis squared left parenthesis y right parenthesis to the power of 5 plus 7 C subscript 6 left parenthesis x right parenthesis left parenthesis y right parenthesis to the power of 6 plus 7 C subscript 7 left parenthesis y right parenthesis to the power of 7 end cell row cell equals x to the power of 7 plus 7 x to the power of 6 y plus 21 x to the power of 5 y squared plus 35 x to the power of 4 y cubed plus 35 x cubed y to the power of 4 plus 21 x squared y to the power of 5 plus 7 x y to the power of 6 plus y to the power of 7 end cell end table
    Thus, the expansion is:

    left parenthesis x plus y right parenthesis to the power of 7 equals x to the power of 7 plus 7 x to the power of 6 y plus 21 x to the power of 5 y squared plus 35 x to the power of 4 y cubed plus 35 x cubed y to the power of 4 plus 21 x squared y to the power of 5 plus 7 x y to the power of 6 plus y to the power of 7
     

    The answer can be found using the Pascal’s triangle. For an expression (x + y)n , we would have n + 1 term.

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