Maths-
General
Easy

Question

open parentheses x to the power of 3 end exponent plus x close parentheses plus open parentheses x to the power of 2 end exponent minus x close parentheses Which of the following is equivalent to the given expression?

  1. x to the power of 5 end exponent minus x to the power of 2 end exponent  
  2. x to the power of 5 end exponent minus x to the power of 4 end exponent plus x to the power of 3 end exponent minus x to the power of 2 end exponent  
  3. x to the power of 3 end exponent plus x to the power of 2 end exponent  
  4. x to the power of 3 end exponent plus x to the power of 2 end exponent plus 2 x  

The correct answer is: x to the power of 3 end exponent plus x to the power of 2 end exponent


    1. The given expression is a Cubic expression wherein the variable with the highest power is 3. We will simplify the given expression to find the correct solution.
    2. Options A & Option B has variables with power 5 which is more than 3. Therefore, Option A & Option B can not be the correct Options.
    Step-by-step solution:-
    (x3 + x) + (x2 -x) = x3 + x + x2 – x -------------------------- (Opening the brackets)
    = x3 + x2 + x - x -------------------------- (Rearranging the variables)
    = x3 + x2 + 0
    = x3 + x2
    Final Answer:-
    Option C i.e. x3 + x2 is the correct Option.
    Note:-
    Alternatively, we can substitute any number in place of x and find the solution of the given expression and the 4 options.
    Eg. Substituting x = 1, we get-
    (x3 + x) + (x2 -x) = 13 + 1 + 12 - 1 -------------------------- (Opening the brackets)
    = 1 + 1 + 1 - 1 -------------------------- (Rearranging the variables)
    = 2
    Option A = x5 - x2
    = 15 - 12
    = 1 - 1
    = 0
    Option B = x5 - x4 + x3 - x2
    = 15 - 14 + 13 - 12
    = 1 - 1 + 1 - 1
    = 0
    Option C = x3 + x2
    = 13 + 12
    = 1 + 1
    = 2
    Option D = x3 + x2 + 2x
    = 13 + 12 + 2(1)
    = 1 + 1 + 2
    = 4
    Hence, Option C is the correct Option.

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