Question

anna subtracted $(7n^{2}-5n + 6)$ from $(5n^{2}+4n - 9)$ as shown below.
$5n^{2}+4n+(-9)$
$\underline{+(-7n^{2})+5n + 6}$
$-2n^{2}+9n+(-3)$
what error did anna make?
○ she did not align like terms correctly.
○ she forgot to use the additive inverse of $(5n^{2}+4n - 9)$.
○ she made a mistake when finding the additive inverse of $(7n^{2}-5n + 6)$.

Explanation:

Step1: Define subtraction as adding inverse

To subtract $(7n^2 - 5n + 6)$ from $(5n^2 + 4n - 9)$, we calculate:
$$(5n^2 + 4n - 9) - (7n^2 - 5n + 6) = (5n^2 + 4n - 9) + (-7n^2 + 5n - 6)$$

Step2: Compare with Anna's work

Anna wrote the second term as $(-7n^2) + 5n + 6$, but the correct additive inverse of $6$ is $-6$.

Step3: Identify the error

Anna incorrectly handled the constant term's sign when finding the additive inverse of $(7n^2 - 5n + 6)$.

Answer:

She made a mistake when finding the additive inverse of $(7n^2 - 5n + 6)$.