Maths-
General
Easy

Question

Find the fifth term of the binomial expansion  left parenthesis x plus y right parenthesis to the power of 5 .

The correct answer is: Thus, the fifth term of the expansion is .


    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 find the fifth term of the binomial expansion of left parenthesis x plus y right parenthesis to the power of 5.
    Step 1 of 2:
    The given expression is left parenthesis x plus y right parenthesis to the power of 5 . Here, the value of n=5.
    Thus, we will have n+1=5+1=6 terms.
    Step 2 of 2:
    Substitute the values in the binomial expansion to get the coefficients:
    left parenthesis x plus y right parenthesis to the power of 5 equals 5 C subscript 0 x to the power of 5 plus 5 C subscript 1 x to the power of 4 left parenthesis y right parenthesis plus 5 C subscript 2 x cubed open parentheses y squared close parentheses plus 5 C subscript 3 open parentheses x squared close parentheses open parentheses y cubed close parentheses plus 5 C subscript 4 left parenthesis x right parenthesis open parentheses y to the power of 4 close parentheses plus 5 C subscript 5 y to the power of 5
    equals x to the power of 5 plus 5 x to the power of 4 y plus 10 x cubed y squared plus 10 x squared y cubed plus 5 x y to the power of 4 plus y to the power of 5
    Thus, the fifth term of the expansion is 5 x y to the power of 4 .
    Note:
    The expansion of  left parenthesis x plus y right parenthesis to the power of nhas n+1 terms while expanding. The answer can be found using the Pascal’s triangle or binomial expansion.

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