Peter has to subtract $(x^2 - 2x - 4)$ from $(x^2 + 3x + 5)$ Here is his working $\begin{align*} (x^2 + 3x + 5) - (x^2 - 2x - 4) &= x^2 + 3x + 5 - x^2 + 2x + 4 \\ &= x + 1 \end{align*}$ Explain what is wrong with Peter’s working. - Edexcel - GCSE Maths - Question 10 - 2022 - Paper 3

Peter's working contains several mistakes:

1. Incorrect Handling of Parentheses: When subtracting the expression $(x^2 - 2x - 4)$, he should have distributed the negative sign across all the terms inside the brackets. This means he should have derived:

   \begin{align*} (x^2 + 3x + 5) - (x^2 - 2x - 4) & = x^2 + 3x + 5 - x^2 + 2x + 4. \end{align*}

   which leads to incorrect subsequent calculations.

2. Collecting Like Terms Properly: He incorrectly simplifies $5 - (-4)$, as that should actually result in $5 + 4 = 9$. This compensated concluding to $x + 1$ is erroneous.

3. Final Result Error: The final simplification lacks proper aggregation of terms, since only adding like terms from each part appropriately will yield the accurate result. Peter needs to take into account all terms after correctly applying the negative sign in front of the subtracted polynomial.