Simplify

Simplify(expr)

simplifies expr

Simplify(expr, option1, option2, ...)

simplify expr with some additional options set

>> Simplify(1/2*(2*x+2))
x+1

>> Simplify(2*Sin(x)^2 + 2*Cos(x)^2)
2

>> Simplify(x)
x

>> Simplify(f(x))
f(x)

>> Simplify(a*x^2+b*x^2)
(a+b)*x^2

Simplify with an assumption:

>> Simplify(Sqrt(x^2), Assumptions -> x>0)
x

For Assumptions you can define the assumption directly as second argument:

>> Simplify(Sqrt(x^2), x>0)
x

>> Simplify(Abs(x), x<0)
Abs(x)

With this “complexity function” the Abs expression gets a “heavier weight”.

>> complexity(x_) := 2*Count(x, _Abs, {0, 10}) + LeafCount(x)

>> Simplify(Abs(x), x<0, ComplexityFunction->complexity)
-x