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

Peter's working contains several mistakes related to the subtraction of polynomials. Firstly, he fails to properly expand the brackets during the subtraction process. The correct procedure would require him to change the signs of the terms within the second polynomial $(x^2 - 2x - 4)$, effectively giving:

$ext{from } (x^2 + 3x + 5) - (x^2 - 2x - 4) ext{ to } (x^2 + 3x + 5) - x^2 + 2x + 4$

This results in: $= x^2 + 3x + 5 - x^2 + 2x + 4$

Next, he should combine like terms correctly. When combining the $3x$ and $2x$, he should not ignore the fact that these should be summed:

after the combination: $3x + 2x = 5x$

Now, if we correctly collect all the terms, we arrive at: $= (3x + 2x) + (5 + 4) = 5x + 9$

Thus, the correct answer is: $5x + 9$

In summary, Peter didn't distribute the negative sign properly and failed to combine the like terms accurately.