 # Solving Equations and Problems Solving

Section 3.1

Simplifying Algebraic
Expressions In algebra letters called variables
represent numbers. The addends of an algebraic expression are
called
the terms of the expression. A term that is only a number is called a constant
term, or simply a constant. A term that contains
a variable is called a variable term.  The number factor of a variable term is called the
numerical coefficient . A numerical coefficient of
1 is usually
not written.  Terms that are exactly the same, except that they
may have different numerical coefficients are
called like terms . Like Terms Unlike Terms A sum or difference of like terms can be
simplified using the distributive
property. Distributive Property

If a, b, and c are numbers, then

ac + bc = (a + b)c

Also,

ac - bc = (a - b)c By the distributive property,

7x + 5x = (7 + 5)x

= 12x

This is an example of combining like terms .

An algebraic expression is simplified when all
like terms have been combined.

The commutative and associative
help simplify expressions. If a, b, and c are numbers, then

a + b = b + a

Commutative Property of Multiplication

a · b = b · a

The order of adding or multiplying two numbers
can be changed without changing their sum or
product
.

The grouping of numbers in addition or
multiplication can be changed without
changing their sum or product. (a + b) + c = a + (b + c)

Associative Property of Multiplication

(a · b) · c = a · (b · c) Examples of Commutative and Associative Properties

 4 + 3 = 3 + 4 Commutative property of Addition 6 · 9 = 9 · 6 Commutative property of Multiplication (3 + 5) + 2 = 3 + (5 + 2) Associative property of Addition (7 · 1) · 8 = 7 · (1 · 8) Associative property of Multiplication
We can also use the distributive property
to multiply expressions. The distributive property says that
and subtraction.

2(5 + x) = 2· 5 + 2 · x = 10 + 2x

or

2(5 – x) = 2· 5 – 2 · x = 10 – 2x

To simply expressions, use the distributive
property first to multiply and then combine
any like terms. Simplify: 3(5 + x) - 17 Apply the distributive property Multiply Combine like terms

 Helpful Hint 3 is not distributed to the -17 since -17 is not within the parentheses .
Finding Perimeter  Perimeter is the distance around the figure. Finding Area   Don’t forget . . .

 Area: • surface enclosed • measured in square units

Perimeter:
• distance around
• measured in units

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