How to evaluate algebraic expressions
Evaluate expressions by substituting known values
Evaluating expressions means that you’ll be replacing or “plugging in” numbers for variables and then simplifying using the order of operations until you arrive at a single number.
Sometimes you’ll be able to plug in the numbers without issue, but there are other times (when there’s multiplication, exponents, or when plugging in a negative number) where you’ll need to plug in the numbers using parentheses.
When in doubt, use parentheses! It’s better to have unnecessary parentheses than to not have parentheses that you actually really need.
How to find the values of algebraic expressions by plugging in known values
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Finding z when you know x and y
Example
Use the given values to solve for ???z???, when ???x=8??? and ???y=3???.
???x-y=z???
Plug in ???8??? for ???x??? and ???3??? for ???y??? to the given equation.
???8-3=z???
Simplify the left side of the equation
???5=z???
Let’s try another example of evaluating expressions.
Example
Use the given values to evaluate the expression, when ???a=2???, ???b=-1???, and ???c=3???.
???abc+c^3+ab???
Plug in ???2??? for ???a???, ???-1??? for ???b???, and ???3??? for ???c???. Remember that ???abc??? means ???a\cdot b\cdot c??? and so we’ll need to use parentheses when plugging in these values.
???(2)(-1)(3)+(3)^3+(2)(-1)???
Now simplify using the order of operations. Exponents first since none of our parentheses are grouping symbols and instead mean multiplication.
???(2)(-1)(3)+27+(2)(-1)???
Multiply left to right.
???-6+27-2???
Add.
???19???