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Easy

Question

Use binomial theorem to expand open parentheses s squared plus 3 close parentheses squared .

The correct answer is: For the expansion of an expression , we would have n+1 terms. This is something you need to keep in mind.


    ANSWER:
    Hint:
    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  , here n greater or equal than 0  .
    We are asked to use binomial theorem to expand open parentheses s squared plus 3 close parentheses to the power of 5 .
    Step 1 of 2:
    The given expression is open parentheses s squared plus 3 close parentheses to the power of 5, here x equals s squared straight & y equals 3 . The value of n=5, hence there are 5+1=6 terms in the expressions.
    Step 2 of 2:
    Substitute the values of open parentheses s squared plus 3 close parentheses to the power of 5 in the binomial equation to get the expansion:
    open parentheses s squared plus 3 close parentheses to the power of 5 equals 5 C subscript 0 open parentheses s squared close parentheses to the power of 5 plus 5 C subscript 1 open parentheses s squared close parentheses to the power of 4 left parenthesis 3 right parenthesis plus 5 C subscript 2 open parentheses s squared close parentheses cubed left parenthesis 3 right parenthesis squared plus 5 C subscript 3 open parentheses s squared close parentheses squared left parenthesis 3 right parenthesis cubed plus 5 C subscript 4 open parentheses s squared close parentheses left parenthesis 3 right parenthesis to the power of 4 plus 5 C subscript 5 left parenthesis 3 right parenthesis to the power of 5equals s to the power of 10 plus 5 open parentheses s to the power of 8 close parentheses left parenthesis 3 right parenthesis plus 10 open parentheses s to the power of 6 close parentheses left parenthesis 9 right parenthesis plus 10 open parentheses s to the power of 4 close parentheses left parenthesis 27 right parenthesis plus 5 open parentheses s squared close parentheses left parenthesis 81 right parenthesis plus left parenthesis 243 right parenthesis
    equals s to the power of 10 plus 15 s to the power of 8 plus 90 s to the power of 6 plus 270 s to the power of 4 plus 405 s squared plus 243
    Thus, the expansion is: open parentheses s squared plus 3 close parentheses to the power of 5 equals s to the power of 10 plus 15 s to the power of 8 plus 90 s to the power of 6 plus 270 s to the power of 4 plus 405 s squared plus 243
    Note:
    For the expansion of an expression left parenthesis x plus y right parenthesis to the power of n,we would have n+1 terms. This is something you need to keep in mind.

    Thus, the expansion is:
    Note:
    For the expansion of an expression , we would have n+1 terms. This is something you need to keep in mind.

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