Symbolic calculations

Algebraic simplifications

x^2 +7x^2+y^2-10x+x(x+1)

Use the command Expand to multiply the terms

Expand[(x^7-3x^2) (x+x^5)^3]

Use Factor to get back

Often you need to replace the  unknown variables by 
solutions, eg after solving equations.

1+x+x^2  /.  x->Pi^2 + 1

Try to put the replacement first and  use it afterwards