1. Now that we have seen some algebraic
expressions, we need to know how to
simplify them.
Vocabulary
Like terms: In an expression, like terms are the
terms that have the same variables, raised to the
same powers (same exponents).
i.e. 4x and -3x or 2y2 and –y2
Coefficient: A constant that multiplies a variable.
i.e. the 3 in 3a or the -1 in –b
2. In algebra we often get very long expressions,
which we need to make simpler. Simpler
expressions are easier to solve!
To simplify an expression we collect like
terms. Like terms include letters that are the
same and numbers.
3. Step One: Write the expression.
4x + 5x -2 - 2x + 7
Collect all the terms together which are alike. Remember that each term
comes with an operation (+,-) which goes before it.
4x, 5x, and -2x
-2 and 7
Simplify the variable terms.
4x+5x-2x = 9x-2x = 7x
Simplify the constant (number) terms.
-2+7 = 5
You have a simplified expression by writing all of the results from
simplifying.
7x + 5
4. 10x – 4y + 3x2 + 2x – 2y
3x2
10x, 2x
-4y – 2y
3x2 + 12x – 6y
Remember you cannot
combine terms with
the same variable but
different exponents.
5. Simplify the following:
5x + 3y - 6x + 4y + 3z
3b - 3a - 5c + 4b
4ab – 2a2b + 5 – ab + ab2 + 2a2b + 4
5xy – 2yx + 7y + 3x – 4xy + 2x
A
A
A
A
10. A variable or algebraic expression is an
expression that consists of one or more
________ and _________ along with one or
more numbers ________ _________. variables
(Note: No _______
sign)
arithmetic operations
equal
To evaluate an expression write the _________,
substitute expression a _______ for each variable, and
_________ the result.
number
simplify
11. In an expression, like __________ terms
are the terms that
have the same ________, variables
raised to the same
________ power
(same exponents).
A coefficient is a number that ________ multiplies
a
variable.
