Which expression can be used to find the difference of the polynomials?
Check the final answer first, then review the worked steps.
Problem
Which expression can be used to find the difference of the polynomials?
Answer
\((4m - 5) + (-6m + 7 - 2n)\)
Step-by-step solution
- Understand the problem: The problem asks to find an equivalent expression for the difference between two polynomials: $(4m - 5)$ and $(6m - 7 + 2n)$. Subtracting a polynomial is the same as adding its additive inverse.
- Rewrite the subtraction as addition: To subtract $(6m - 7 + 2n)$ from $(4m - 5)$, we can rewrite the expression as $(4m - 5) - (6m - 7 + 2n)$. This is equivalent to adding the opposite of the second polynomial: $(4m - 5) + (-(6m - 7 + 2n))$.
- Distribute the negative sign: Distribute the negative sign to each term inside the second parenthesis: $-(6m - 7 + 2n) = -6m + 7 - 2n$.
- Form the equivalent addition expression: Now, substitute this back into the expression from step 2: $(4m - 5) + (-6m + 7 - 2n)$. This expression represents the difference of the original polynomials.
- Combine like terms (optional, for verification): To verify, we can simplify this expression. Combine the $m$ terms: $4m - 6m = -2m$. Combine the constant terms: $-5 + 7 = 2$. Combine the $n$ terms: $-2n$. So, the simplified difference is $-2m + 2 - 2n$. The expression $(4m - 5) + (-6m + 7 - 2n)$ is the correct representation of the difference.