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Use the binomial theorem to expand the expressions: left parenthesis 3 x minus 0.2 right parenthesis cubed

hintHint:

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 comma text  here  end text n greater or equal than 0.
We are asked to find the expansion of left parenthesis 3 x minus 0.2 right parenthesis cubed using Binomial theorem.

The correct answer is: 0.008


     Step 1 of 2:
    The given expression is left parenthesis 3 x minus 0.2 right parenthesis cubed . Here , the value of n=3 so the number of terms are 3+1=4. The values are x = 3x & y = -0.2
    Step 2 of 2:
    Substitute the values 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 left parenthesis 3 x minus 0.2 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 negative 0.2 right parenthesis plus 3 C subscript 2 left parenthesis 3 x right parenthesis left parenthesis negative 0.2 right parenthesis squared plus 3 C subscript 3 left parenthesis negative 0.2 right parenthesis cubed end cell row cell equals 27 x cubed plus 3 open parentheses 9 x squared close parentheses left parenthesis negative 0.2 right parenthesis plus 3 left parenthesis 3 x right parenthesis left parenthesis 0.04 right parenthesis plus left parenthesis negative 0.008 right parenthesis end cell row cell equals 27 x cubed minus 5.4 x squared plus 0.36 x minus 0.008 end cell end table
    Thus, the expansion is left parenthesis 3 x minus 0.2 right parenthesis cubed equals 27 x cubed minus 5.4 x squared plus 0.36 x minus 0.008

    The answer can also be found using the Pascal’s triangle. For the expansion of the expression (x + y)n , we would consider the (n+1)th row in the triangle.

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