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Question

Use binomial theorem to expand left parenthesis x minus 3 right parenthesis to the power of 4 .

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 left parenthesis x minus 3 right parenthesis to the power of 4.
    Step 1 of 2:
    Here, the value of n=4. So, the combination permutation we would use is .
    We would have 4+1=5 terms in the expansion of the expression left parenthesis x minus 3 right parenthesis to the power of 4.
    Step 2 of 2:
    Substitute the values of left parenthesis x minus 3 right parenthesis to the power of 4 in the binomial expansion:
    left parenthesis x minus 3 right parenthesis to the power of 4 equals 4 C subscript 0 x to the power of 4 plus 4 C subscript 1 left parenthesis x right parenthesis cubed left parenthesis negative 3 right parenthesis plus 4 C subscript 2 left parenthesis x right parenthesis squared left parenthesis negative 3 right parenthesis squared plus 4 C subscript 3 left parenthesis x right parenthesis left parenthesis negative 3 right parenthesis cubed plus 4 C subscript 4 left parenthesis negative 3 right parenthesis to the power of 4
    equals x to the power of 4 plus 4 left parenthesis x right parenthesis cubed left parenthesis negative 3 right parenthesis plus 6 x squared left parenthesis 9 right parenthesis plus 4 left parenthesis x right parenthesis left parenthesis negative 27 right parenthesis plus 1 left parenthesis negative 3 right parenthesis to the power of 4
    equals x to the power of 4 minus 12 x cubed plus 54 x squared minus 108 x plus 81
    Thus, the expansion is:left parenthesis x minus 3 right parenthesis to the power of 4 equals x to the power of 4 minus 12 x cubed plus 54 x squared minus 108 x plus 81
    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.

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