Simplify algebraic expressions by substituting given values

In algebra we will often need to simplify an expression to make it easier to use. There are three basic forms of simplifying which we will review here. The first form of simplifying expressions is used when we know what number each variable in the expression represents. If we know what they represent we can replace each variable with the equivalent number and simplify what remains using order of operations. Example `p(q+6)` when `p=3` and `q=5`
Expression `p(q+6)`
Replace `p` with `3` and `q` with `5` `=(3)((5) + 6)`
Evaluate parenthesis `=(3)(11)`
Multiply `=33`
Whenever a variable is replaced with something, we will put the new number inside a set of parenthesis. Notice the 3 and 5 in the previous example are in parenthesis. This is to preserve operations that are sometimes lost in a simple replacement. Sometimes the parenthesis won’t make a difference, but it is a good habbit to always use them to prevent problems later. Example `x+zx(3−z)(x/3)` when `x=−6` and `z=−2`
`x+zx(3−z)(x/3)`
Replace all `x`′s with `6` and`z`′s with `-2` `=(−6)+(−2)(−6)(3−(−2))((−6)/3)`
Evaluate parenthesis `=−6+(−2)(−6)(5)(−2)`
Multiply left to right `=−6+12(5)(−2)`
Multiply left to right `=−6+60(−2)`
Multiply `=−6−120`
Subtract `=-126`