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Simplify sqrt(108) B. sqrt(12)-sqrt(27) C. 6sqrt(3)-5sqrt(3) D. 6sqrt(3)-sqrt(2) 2.Solve\;x2+x−12=0 B.\;x2+x−12−6=0 C.\;x2+2x−12−6=0 D.\;x2−x−12=0

Mathematics

ScanSolve AI Answer

Answer

C

Step-by-step solution

4 steps

Let's expand the expression.

  1. Write down the expression to be expanded.

    (2x−5)(x−3)(2x-5)(x-3)
  2. Use the distributive property (or FOIL method) to multiply the terms.

    Multiply the first term of the first binomial by each term of the second binomial:

    2x(x)+2x(−3)=2x2−6x2x(x) + 2x(-3) = 2x^2 - 6x

    Multiply the second term of the first binomial by each term of the second binomial:

    −5(x)+−5(−3)=−5x+15-5(x) + -5(-3) = -5x + 15
  3. Combine the results from Step 2.

    2x2−6x−5x+152x^2 - 6x - 5x + 15
  4. Combine like terms*.

    2x2+(−6x−5x)+152x^2 + (-6x - 5x) + 15 2x2−11x+152x^2 - 11x + 15

    Comparing this with the given options, the correct option is C.

    The expanded form is C. 2x2−11x+15\boxed{\text{C. } 2x^2 - 11x + 15}.

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