Maths question

Hi, can someone check these workings for me please and let me know where I’ve made any mistakes

Ah, the good ol' classic. (a+b)^2 is NOT a^2 + b^2...

Though I'm a bit unsure what problem you are trying to solve.

There’s two separate ones, each written at the top of the page

Which question are you referring to?

Both of them. You can't just "distribute the exponent" over sums.
To put it specifically, you have made the classic error on the first line for both problems.

Both of them. You can't just "distribute the exponent" over sums.
To put it specifically, you have made the classic error on the first line for both problems.

Got to this which is correct so thank you!

It probably is, but if youd simplified the bracket first after a couple of lines youd have
x(x^2+x-1)^2
Then expanding the square is trivial. They probably wanted you to think ahead first, rather than expanding and doing a lot of work.

What do you mean?

Get the initial bracket into that form?

Yes. You can obv do the division which gives exponents #/2 and the exponents are in an arithmetic sequence, ... all of which Id presume youre meant to spot.

Generally you want to simplify as much as possible before expanding. In this case, its a bit artificial as the expression has been deliberately obfuscated but its not hard to spot that it simplifies.

Great thanks a lot! I presume practising helps spot these quicker, do you know any good websites with maths questions?

Tbh, the numerator is a hidden quadratic so its a ~hard gcse question so you were probably expected to spot that. As much as anything its getting in the habit of thinking about what the first steps can be and quickly evaluating (mentally?) a couple of lines to see which gives, rather than ploughing ahead with the first thing that comes to mind. Here, it would be fairly obvious that expanding the square would be laborious/error prone whereas the expression in the bracket would siimplify considerably so that was the obv first step.

For extra questions/practice, Id ask your teacher first, also drfrost has a large question bank which is graded by difficulty. For others, google something like
simplifying challenging algebraic expressions worksheet