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