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General
Easy

Question

Expand left parenthesis 3 x plus 4 y right parenthesis cubed using binomial theorem.

The correct answer is: Thus, 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 binomial expansion of left parenthesis 3 x plus 4 y right parenthesis cubed using binomial theorem.
    Step 1 of 2:
    The given expression is  . left parenthesis 3 x plus 4 y right parenthesis cubed text . Here  end text x equals 3 x straight & y equals 4 y. The value of n=3. Thus, the number of terms would be n+1=3+1=4.
    Step 2 of 2:
    Substitute the values in the expression to get the terms of the binomial expansion;
    left parenthesis 3 x plus 4 y right parenthesis cubed equals 3 C subscript 0 left parenthesis 3 x right parenthesis cubed plus 3 C subscript 1 left parenthesis 3 x right parenthesis squared left parenthesis 4 y right parenthesis plus 3 C subscript 2 left parenthesis 3 x right parenthesis left parenthesis 4 y right parenthesis squared plus 3 C subscript 3 left parenthesis 4 y right parenthesis cubed
    equals 1 open parentheses 27 x cubed close parentheses plus 3 open parentheses 9 x squared close parentheses left parenthesis 4 y right parenthesis plus 3 left parenthesis 3 x right parenthesis open parentheses 16 y squared close parentheses plus 1 open parentheses 64 y cubed close parentheses
    equals 27 x cubed plus 108 x squared y plus 144 x y squared plus 64 y cubed
    Thus, the expansion is:left parenthesis 3 x plus 4 y right parenthesis cubed equals 27 x cubed plus 108 x squared y plus 144 x y squared plus 64 y cubed
    Note:
    The answer can be found using the Pascal’s triangle. For left parenthesis x plus y right parenthesis to the power of n , we would consider the (n+1) th row as the coefficients.

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