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

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.

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

10x – 4y + 3x2 + 2x – 2y3x2

10x, 2x-4y – 2y

3x2 + 12x – 6y

Remember you cannot combine

terms with the same variable but

different exponents.

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

Simplify the following:1. 5x + 3y - 6x + 4y + 3z

5x, -6x3y, 4y3z-x + 7y + 3z

Simplify the following:2. 3b - 3a - 5c + 4b

3b, 4b-3a-5c-3a + 7b – 5c

Simplify the following:3. 4ab – 2a2b + 5 – ab + ab2 + 2a2b + 4

4ab, -ab-2a2b, 2a2b5, 4ab2

3ab + ab2 + 9

Simplify the following:4. 5xy – 2yx + 7y + 3x – 4xy + 2x

5xy, -2yx, -4xy 7y3x, 2x-xy + 7y + 5x

A variable or algebraic expression is an expression that consists of one or more ________ and _________ along with one or more ________ _________. (Note: No _______ sign)

To evaluate an expression write the _________, substitute a _______ for each variable, and _________ the result.

numbers variables

arithmetic operations

equal

expression number

simplify

In an expression, __________ are the terms that have the same ________, raised to the same ________ (same exponents).

A coefficient is a number that ________ a variable.

like terms

variables

power

multiplies