Maths-
General
Easy

Question

Explain why the middle term left parenthesis x plus 5 right parenthesis squared is 10x.

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 explain why the middle term (x + 5)2 is 10x.

The correct answer is: = x2 + 10x + 25



    Step 1 of 1:
    The given expression is: (x + 5)2
    Here, a=x and b=5.
    Here, the middle term is 10x because while expanding you have the form,

    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 x plus 5 right parenthesis squared equals 2 C subscript 0 x squared plus 2 C subscript 1 left parenthesis 5 right parenthesis left parenthesis x right parenthesis plus 2 C subscript 2 5 squared end cell row cell equals x squared plus 2 left parenthesis 5 right parenthesis left parenthesis x right parenthesis plus 5 squared end cell row cell equals x squared plus 10 x plus 25 end cell end table
     

    The expansion of left parenthesis x plus y right parenthesis squared equals x squared plus 2 x y plus y squared is one of the standard and widely used polynomial identity.

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