Question

anna subtracted \\((7n^2 - 5n + 6)\\) from \\((5n^2 + 4n - 9)\\) as shown below.

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$$\begin{aligned} &5n^2 + 4n + (-9) \\\\ + &(-7n^2) + 5n + 6 \\\\ \\hline &-2n^2 + 9n + (-3) \\end{aligned}$$

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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:

⚡ Using what you learned: adding and subtracting polynomials

Step 1: Set up the subtraction

To subtract \( (7n^2 - 5n + 6) \) from \( (5n^2 + 4n - 9) \), we write the expression as:

$$ (5n^2 + 4n - 9) - (7n^2 - 5n + 6) $$

Step 2: Find the additive inverse of the subtracted polynomial

To subtract, we add the additive inverse (opposite) of each term in the polynomial being subtracted:

$$ -(7n^2 - 5n + 6) = -7n^2 + 5n - 6 $$

Step 3: Compare with Anna's work

Anna wrote the second line of her addition as:

$$ +(-7n^2) + 5n + 6 $$

She correctly changed the signs of \( 7n^2 \) to \( -7n^2 \) and \( -5n \) to \( 5n \), but she did not change the sign of the constant term \( 6 \) to \( -6 \).

Therefore, she made a mistake when finding the additive inverse of \( (7n^2 - 5n + 6) \).

Answer:

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