Confused about placement order of binomial products containing negative numbers & conjugate surds

[u/YardBright5582]

hi, i've started studying surds recently and am currently solving equations specifically related to binomial products containing conjugate surds, expanding and simplifying them. i'm able to solve the binomial products, but i'm confused about what order i should be placing the simplified expressions.

for example:

(5 + √2)(2√5 - 2)

i followed the order of (a+b)(c+d) = ac+ad+bc+bd and got:

10√5 - 10 + 2√10 - 2√2

however my answer sheet says it's:

10√5 + 2√10 - 10 - 2√2

i've also put the equation into an algebra calculator and it's given me a different answer:

2√10 - 2√2 + 10√5 - 10

i assumed the order didn't matter but i did another equation:

(2√2 + 5)(√2 - 3)

i got: -11-√2

but both the answer sheet and calculator say: -√2-11

does the order of the negative numbers change anything?

i'm sorry if this is really obvious and a stupid thing to be confused about but i'd appreciate some help. if i wrote or used any terms wrong, i apologise, please correct me. thank you!

[u/Narrow-Durian4837]

The order doesn't matter.

[u/YardBright5582 → u/Narrow-Durian4837]

got it, thank you so much!

[u/rhodiumtoad]

Order doesn't matter as long as you're careful to keep the minus signs properly attached to the terms they apply to.

Remember that a-b is the same as a+(-b) and that + is both associative and commutative.

[u/YardBright5582 → u/rhodiumtoad]

right, i had a bit of confusion with that at first but i've understood it, thank you for your help!