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Simplification

There are various ways to get rid of parentheses, when you are simplifying an expression.
Parentheses that are added to something can be removed without further ado.
a+(b+c)=a+b+c

Parentheses that are subtracted from something can be removed as long as all plus signs inside the parentheses are exchanged with minus signs and all minus signs are exchanged with plus signs.

a-(b+c)=a-b-c

The Distributive Property
When multiply something by an expression inside parentheses, it has to be multiplied by each part inside the parentheses.
a*(b+c)=a*b+a*c

That also applies when two sets of parentheses are multiplied together; each part inside the one set of parentheses is multiplied by each part in the other set of parentheses.
(a+b)*(c+d)=a*c+a*d+b*c+b*d=ac+ad+bc+bd

For examples, we want to simplify the expression:

x+2x(x+1)

First 2x is multiplied by the parentheses:

x+2x(x+1)=x+2x*x+2x*1=x+2x^2+2x

Then we add all parts of the same type:

x+2x^2+2x=2x^2+3x

Please note that the order of the arithmetic operation applies here. First we do the multiplying by the parentheses, and then we do the addition.