1. Simplify expressions .
2.Identify terms and numerical coefficients.
3.Identify like terms .
4. Combine like terms .
5.Simplify expressions from word phrases.
Objective 1
Simplify expressions.
EXAMPLE 1
Simplifying Expressions
Simplify each expression.
Solution :
Objective 2
Identify terms and numerical coefficients.
A term is a number, a variable, or a product or
quotient of numbers and variables raised to powers , such as
Terms
In the term 9x, the numerical coefficient, or simply coefficient,
of the variable x is 9. In the term −8m2n the numerical coefficient of
m 2n is −8
It is important to be able to distinguish between terms
and factors. For example, in the expression 8x3 + 12x2, there are
two terms , 8x3 and 12x2. Terms are separated by a + or −sign. On the other
hand, in the one-term expression (8x3)(12x2), 8x3 and 12x2 are factors .
Objective 3
Identify like terms.
Terms with exactly the same variables that have the same
exp onents are like terms. For example, 9m and 4m have the same variable
and are like terms.
The terms −4y and 4y2 have different exponents and are
unlike terms.
Like terms
Unlike terms
Objective 4
Combine like terms.
Recall the distributive property :
This statement can also be written “backward”as
This form of the distributive property may be used to find
the sum or difference of like terms .
Using the distributive property in this way is called
combining like terms.
EXAMPLE 2
Combining Like Terms
Combine like terms in each expression.
Solution:
Cannot be combined
EXAMPLE 3
Simplifying Expressions Involving Like Terms
Simplify each expression.
Solution:
Constants are like terms and may be combined.
Objective 5
Simplify expressions from word phrases.
EXAMPLE 4
Translating Words to a Mathematical Expression
Translate to a mathematical expression and simplify.
Three times a number, subtracted from the sum of the
number and 8.
Solution:
Remember, we are dealing with an expression to be simplified, not an equation to
be solved .
