PODUse mental math to solve:

basic advanced

8 × 34

8(30) + 8(4)

240 + 32

272

7 × 231

7(200) + 7(30) + 7(1)

1400 + 210 + 7

1617

PODWrite the expression in simplest form:

4p −7 + 6p +10

4p + (-7) + 6p +10

4p + 6p + (-7) + 10

10p + 3

PODWrite the expression in simplest form:

-5x + 3 + 7x − 8

-5x + 3 + 7x + (-8)

-5x + 7x + 3 + (-8)

2x + 3 + (-8)2x + (-5)

Simplify Algebraic Expressions

When addition or subtraction signs separate an algebraic expression into parts, each part is called a term. The numerical factor of a term that contains a variable is called a coefficient of the variable.

Like terms contain the same variables to the same powers. For example 3x and 7x are like terms. So are 8xy2 and 12xy2.

A term without a variable is called a constant.

-4x + 12 + x

three terms

constant

like terms

6n − 7n − 4 + nexample

Identify the terms: 6n, 7n, 4, n

Identify the like terms: 6n, 7n, n

Identify the coefficients: 6, 7, 1

Identify the constants: 4

An algebraic expression is in simplest form if it has no like terms and no parenthesis.

Example:

Write 4y + y in simplest form4y + y = 4y + 1y multiplicative identity property; y=1y

5y

Example:

Write 7x − 2 − 7x + 6 in simplest form

7x − 2 − 7x + 6 = 7x + (-2) + (-7x) + 6 Definition of subtraction

= 7x + (-7x) + (-2) + 6 Commutative Property

= (0)x + 4 = 0 + 4 = 4

Multiplicative Property of Zero

Whiteboard time

Identify the terms, like terms, coefficients, and constants in each expression.

9y − 4 − 11y + 7terms: 9y, 4, 11y, 7

like terms: 9y and -11y, -4 and 7

coefficients: 9, 11

constants: 4, 7

Whiteboard time

Identify the terms, like terms, coefficients, and constants in each expression.

3x + 2 − 10 − 3xterms: 3x, 2, 10, 3x

like terms: 3x and 3x,

coefficients: 3, 3

constants: 2, 10

Whiteboard time

Write the expression in simplest form

4z − z

4z − 1z

3z

Whiteboard time

Write the expression in simplest form

6 − 3n + 3n

6 − 0

6

Whiteboard time

Write the expression in simplest form

2g − 3 + 11 − 8g2g + (-3) + 11 + (-8g)

2g + (-8g) + (-3) + 11

-6g + 8

2g + (-8g) + 8