Johnny wonders if he can relate the sum and difference of two polynomials, using the equations shown. -(K + F) = K - F.

Question

Are the two expressions shown equivalent to each other? What evidence supports or disproves the statement? Pick the statement below that clearly explains your answer, remembering to justify by listing the property used.

YES - the two expressions are equivalent because -(K + F) = -K + -F I used the negative property of multiplication to solve.

NO - they are not equivalent because -(K + F) = -K + -F. I used the Distributive Property to simplify the left side.

YES - they are equivalent because -(K + F) = -K + F and then you can switch the - to the F. I used the Commutative Property to change the signs of the K and the F.

NO - they are not equivalent because -(K + F) = -K + F and that is not the correct way it is written above. I used the Distributive Property.

Answer 1

The correct answer is:

NO - they are not equivalent because -(K + F) = -K + F and that is not the correct way it is written above. I used the Distributive Property.

Justification:

Using the Distributive Property, we can distribute the negative sign across the parentheses on the left side:

\[ -(K + F) = -K - F \]

This means the left side simplifies to \(-K - F\).

On the right side of the original equation \(K - F\):

\[ K - F \]

The simplified expressions are:

• Left side: \(-K - F\)
• Right side: \(K - F\)

Clearly, \(-K - F\) is not equivalent to \(K - F\). Thus, the two expressions are not equivalent, confirming the correct choice.