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Parentheses

Parentheses can be used to separate groupings of symbols in mathematics. They can indicate that some operations of a mathematical problem must be carried out before any other.
Sometimes parentheses are redundant. Sometimes they are essential to the way the calculation is done.

Arithmetical operations are always carried out in the following order: exponents, multiplication/division, addition/subtraction.

If you want, for instance, the subtraction in an expression to be carried out before the multiplication in the same expression, you must use parentheses to show that you are changing the order of the arithmetical operations.

Properties of parentheses

PropertyExplanation
a+(b-c+d) = a+b-c+dAll terms inside the parentheses are added to a
a-(-b+c-d) = a+b-c+dAll terms inside the parentheses are subtracted from a.
Please note the signs in front of each term. If you subtract a negative term
it is the same as adding. For example: a-(-b) = a--b = a+b
a×(b-c+d) = a·b-a×c+a×dEach term inside the parentheses is multiplied by a
(a+b)×(c-d) = a×c-a×d+b×c-b×dEach term in the first parentheses is multiplied by each term in the second
parentheses
(a+b)2 = a2+b2+2×a×bThe square of the terms in parentheses is carried out the same way as above,
because (a+b)2 = (a+b)×(a+b) =a×a+a×b+b×a+b×b.
It can then be simplified, because a×a=a2 ,
b×b=b2 and a×b+b×a = 2×a×b
(a-b)2 = a2+b2-2×a×bThe same as above
(a+b)×(a-b) = a2-b2The same as the formula (a+b)×(c-d), but since we get a×a-a×b+b×a-b×b,
-a×b and b×a will eliminate each other by the simplification.