2. Objective 1
Simplify expressions.
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3. Simplifying Expressions
EXAMPLE 1
Simplifying Expressions
Simplify each expression.
Solution:
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4. Identify terms and numerical coefficients.
Objective 2
Identify terms and numerical coefficients.
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5. 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
, , , , , and 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 m2n is −8.
It is important to be able to distinguish between terms and factors. Consider the following expressions.
This expression has two terms, and
Terms are separated by a + or − symbol.
This is a one-term expression.
The factors and are multiplied.
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6. Objective 3
Identify like terms.
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7. Identify like terms. and and Like terms and and Unlike terms
Terms with exactly the same variables that have the same exponents 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.
and and Like terms
and and Unlike terms
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8. Objective 4
Combine like terms.
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9. Combine like terms. Recall the distributive property:
This statement can also be written “backward” as
This last 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.
Remember that only like terms may be combined.
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10. Combine like terms in each expression.
EXAMPLE 2
Combining Like Terms
Combine like terms in each expression.
Solution:
Cannot be combined
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11. Simplifying Expressions Involving Like Terms
EXAMPLE 3
Simplifying Expressions Involving Like Terms
Simplify each expression.
Solution:
Constants are like terms and may be combined.
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