Is -2x^2+5x equivalent to 5x-2(x^2+6)+12

The answer is:  Yes;  "{-2x² + 5x}" is equivalent to "{5x − 2(x² + 6) + 12}" .

Explanation:

The question asks:

    "Is {-2x² + 5x} equivalent to {5x − 2(x² + 6) + 12} ?"

First, we need to simplify the "second expression" ; then rewrite the "second expression; then rewrite the question;

The second expression:  {5x - 2(x² + 6) + 12} ;

Let us simplify and rewrite.

First, let us expand the:  -2(x² + 6) ;

Note:  The distributive property of multiplication:

    a(b+c) = ab + ac ;
    a(b−c) = ab − ac ;

          As such:  -2(x² + 6) = -2*x² + (-2)*6 = -2x² + (-12) = -2x² − 12 ; 

       So we rewrite: "{5x − 2(x² + 6) + 12} " ;  as:

{5x − 2x² − 12 + 12} = 5x − 2x²
 = 5x + (-2x²) = -2x² + 5x; (rewrite with highest degree polynomial first);

So now, we can rewrite the ORIGINAL question:

   "Is {-2x² + 5x} equivalent to {-2x² + 5x} ?"

The answer is: Yes!  These values are equal; and as such, are equivalent.

So, the original question is: 

   "Is {-2x² + 5x} equivalent to {5x − 2(x² + 6) + 12} ? 

The answer is:  Yes;  "{-2x² + 5x}" is equivalent to "{5x − 2(x² + 6) + 12}" .

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