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 <span>− ac ; _________________________________________________________ As such: </span>-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}" . ___________________________________________________________