Maths-
General
Easy

Question

Use binomial theorem to expand (s2 + 3)5

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 ≥ 0 . We are asked to use binomial theorem to expand (s2 + 3)5 .

The correct answer is: 243



    Step 1 of 2:
    The given expression is (s2 + 3)5  , here x = s2 & y = 3 . The value of n=5, hence there are 5+1=6 terms in the expressions.
    Step 2 of 2:
    Substitute the values of (s2 + 3)5 in the binomial equation to get the expansion:

    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 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 5 end cell row cell equals 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 end cell row cell 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 end cell end table
    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
     

    For the expansion of an expression (x + y)n , we would have n+1 terms. This is something you need to keep in mind.

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