SOLUTION: when multiplying two polynomials, what fundamental property do you use repeatedly? Also, why is it necessary to study the order of operations and the laws of operations before you

Question 2098: when multiplying two polynomials, what fundamental property do you use repeatedly? Also, why is it necessary to study the order of operations and the laws of operations before you begin to solve equations?
Thank you!
Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
there are very few basic rules in algebra, but things like the laws of association and commutation are important eg where a(b+c) then we get ab + ac etc. These rules usually are discussed in the very first pages of algebra, so look there for a much more in-depth discussion. My thoughts are purely from memory, adled by tiredness on a Sunday evening.
The order of processes is very important since 2-3x4 could be -1x4 = -4 OR could be 2-12 = -10. Which one? The rule "do it in the order you see it" is SO SO SO SO BADLY WRONG. The order you do ANY calculation is BODMAS...Brackets first, then OF (????), then DIVISION (d) THEN MULTIPLICATION (m) then ADDITION (a) then SUBTRACTION (s)...this order is easier than that, since m and d are opposites of each other, so their order do not matter and a and s are also opposites of each other, so their order does not matter. WHAT MATTERS IS THAT YOU DO m or d BEFORE a or s
So, back to my trivial example above...the correct order is the multiplication first, so 2-12...then we get -10.
To make sure that people remember this, a lot of maths uses brackets, since a bracket takes precedence over anything else...so we would write 2-(3x4), so that you knew!.
Hope that helps.
jon
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