Chapter 1: Tools of Algebra1-2: Algebraic Expressions

Essential Question: How is the distributive property useful in simplifying expressions?

1-2: Algebraic Expressions Definitions

A symbol (usually a letter) that represents one or more numbers is called a variable

An expression that contains one or more variables is called an algebraic expression or variable expression

You evaluate an expression by substituting numbers for the variable in an expression

1-2: Algebraic Expressions Evaluating an Algebraic Expression

Evaluate a – 2b + ab for a = 3 and b = -1

1-2: Algebraic Expressions Evaluating an Algebraic Expression

Evaluate a – 2b + ab for a = 3 and b = -1

Substitute the letters in the equation for their numerical value a – 2b + ab (3) – 2(-1) + (3)(-1)

1-2: Algebraic Expressions Evaluating an Algebraic Expression

Evaluate a – 2b + ab for a = 3 and b = -1

Substitute the letters in the equation for their numerical value a – 2b + ab (3) – 2(-1) + (3)(-1)

Use PEMDAS 3 + 2 – 3 5 – 3 2

1-2: Algebraic Expressions Evaluating an Algebraic Expression with

Exponents Evaluate -x2 – 2(x + 1) for x = 3

1-2: Algebraic Expressions Evaluating an Algebraic Expression with

Exponents Evaluate -x2 – 2(x + 1) for x = 3

Solved no differently. First substitute -x2 – 2(x + 1) -(3)2 – 2((3) + 1)

1-2: Algebraic Expressions Evaluating an Algebraic Expression with

Exponents Evaluate -x2 – 2(x + 1) for x = 3

Solved no differently. First substitute -x2 – 2(x + 1) -(3)2 – 2((3) + 1)

Then use PEMDAS -(3)2 – 2(4) -9 – 2(4) -9 – 8 -17

1-2: Algebraic Expressions Evaluating using word problems

The expression -0.3y + 61 models the percent of eligible voters who voted in presidential elections from 1960 to 2000. In the expression, y represents the number of years since 1960. Find the approximate percentage of eligible voters who voted in 1988.

1-2: Algebraic Expressions Evaluating using word problems

The expression -0.3y + 61 models the percent of eligible voters who voted in presidential elections from 1960 to 2000. In the expression, y represents the number of years since 1960. Find the approximate percentage of eligible voters who voted in 1988.

Since we’re looking for the year 1988, and ‘y’ represents the number of years since 1960, we’ll use 1988-1960 = 28 for y in the equation -0.3(28) + 61 -8.4 + 61 = 52.6 So about 52.6% of eligible voters voted in 1988.

1-2: Algebraic Expressions Some more definitions

A number, variable, or the product of numbers and variables is called a term

If there is a number involved in the term, it is called a coefficient

Terms that share the same variable parts can be combined

Some examples: 3r2 & -r2

-2xy3 & 3xy3

When like terms are combined (added/subtracted), only the coefficient is changed.

1-2: Algebraic Expressions Some properties for simplifying expressions

Subtraction a – b = a + (-b)

Division

The rest (page 13 of your book) are pretty self-explanatory

1aa b a

b b

1-2: Algebraic Expressions Combining Like Terms

3k – k

5z2 – 10z – 8z2 + z

–(m + n) + 2(m – 3n)

1-2: Algebraic Expressions Combining Like Terms

3k – k 3k – 1k 2k

5z2 – 10z – 8z2 + z

–(m + n) + 2(m – 3n)

1-2: Algebraic Expressions Combining Like Terms

3k – k 3k – 1k 2k

5z2 – 10z – 8z2 + z 5z2 – 8z2 – 10z + 1z (just reordered for clarity) -3z2 – 9z

–(m + n) + 2(m – 3n)

1-2: Algebraic Expressions Combining Like Terms

3k – k 3k – 1k 2k

5z2 – 10z – 8z2 + z 5z2 – 8z2 – 10z + 1z (just reordered for clarity) -3z2 – 9z

–(m + n) + 2(m – 3n) -1(m + n) + 2(m – 3n) (distribute) -1m – 1n + 2m – 6n 1m – 7n

1-2: Algebraic Expressions Assignment

Page 15 Problems 2-36 (even problems)