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Order of operations

When following the order of operations with for example:

3-cos^2(X)+6cos^2(X)=0

Why can we combine the cos^2(x) even though the 3-cos^2(x) should come first by the order of BIDMAS?

Reply 1

Squirtle.U

Original post by JakeRStudent

When following the order of operations with for example:

3-cos^2(X)+6cos^2(X)=0

Why can we combine the cos^2(x) even though the 3-cos^2(x) should come first by the order of BIDMAS?

Brackets,
Indices,
Division and Multiplication,
Addition and Subtraction

they are on the same level so doesn't matter which order you do them in
[3-cos^2(X)+6cos^2(X)]

Reply 2

JakeRStudent

Original post by Squirtle.U

Brackets,
Indices,
Division and Multiplication,
Addition and Subtraction

they are on the same level so doesn't matter which order you do them in
[3-cos^2(X)+6cos^2(X)]

Is the rule not if theyre on the same level you do them left to right?

For example 5-6+2 is not the same as 5-(6+2)?

Reply 3

Han-Mingi

Original post by JakeRStudent

Is the rule not if theyre on the same level you do them left to right?

For example 5-6+2 is not the same as 5-(6+2)?

No but remember 3 is a constant which has no affect on the cos^2(X)'s, another way to see this is in algebraic form..
Let Y=cos^2(X)
3-cos^2(X)+6cos^2(X)
Replacing the cos^2(X) with Y becomes
3-Y+6Y
This is a simple enough algebra
The result is
3+5Y
Now all you do is replace cos back in
Hence
3+5cos^2(X)

Reply 4

Squirtle.U

Original post by JakeRStudent

Is the rule not if theyre on the same level you do them left to right?

For example 5-6+2 is not the same as 5-(6+2)?

It is left to right if on the same level. However in your example you changed the sign of the "2" by putting it in brackets.
...
It may help to think of adding minus 6 instead subtracting 6