Chapter 2

LIKE TERMS

1. Terms that have the same variables with the same exponents are like terms. 2. Constants terms are also like terms. EXAMPLE: In 5x+3x+9y+8-3, 5x and 3x are like terms AND 8 and 3 are like terms. Like terms can be combined to simplify the expression. Combining like terms simplifies this example to 8x+9y+5.

Combine like terms to simplify the expression: 7x+3x+x+5-3

11x+2

Combine like terms to simplify the expression: 4(3x-6)+5x+20

4(3x-6)+5x+20 12x-24+5x+20 17x-4

Combine like terms to simply the expression: 3a+9b+4c+6a+5b+8c+7+2+1

9a+14b+12c+10

CONSTANT TERM

A number with no variable. EXAMPLE: In 4x+3y+5+1, 5 and 1 are constant terms.

TERM

A number, variable, product, or quotient in an expression. A term is not a sum or difference. EXAMPLE: In 6x+5x+3+2, there are four terms, 6x, 5x, 3, and 2.

Which property allows you to write 3+(7+8)=(3+7)+8?

Associative Property of Addition

Which property allows you to write (6*2)(7)=(2*7)(6)?

Associative Property of Multiplication

What are the coefficients in 3x+x+2

Both 3 and 1 are coefficients in this expression.

Which property allows you to write 3+4+9=4+3+9?

Commutitive Property of Addition

Which property allows you to write (7)(9)=(9)(7)?

Commutitive Property of Multiplication

TRUE OR FALSE. In 8x+4x+3+1, 8 and 4 are the constant terms.

FALSE. 3 and 1 are the constant terms in this expression. 8 and 4 are coefficients.

True or False. In 7y+3y+4+9, 4 and 9 are the coefficients.

FALSE. 7 and 3 are the coefficients. 4 and 9 are constants.

True or False. In 2x+8x+3+4, the terms are 3 and 4.

FALSE. The terms are 2x, 8x, 3, and 4.

True or False. In 3x+4x+7, the terms are 3x and 4x.

FALSE. The terms are 3x, 4x, and 7.

True or False: 6(5x+4)=30x+4.

False. The 6 must be distributed to both addends in the expression. The correct answer is 30x+24.

Which property allows you to write (4)(1)=4?

Identity Propery of Multiplication

Identity Property of Addition

If you add zero to a number, the sum is the same as that given number. EXAMPLE: x+0=x

Identity Property of Multiplication

If you multlply a number by 1, the product is the same as the given number. EXAMPLE: 1x=x

What are the like terms in the following expression: 4a+7b+3a+5c+9+6?

Like terms are: 4a and 3a AND 9 and 6

What are the like terms in the following expression: 4x+x+3+1?

Like terms are: 4x and x AND 3+1

What are the like terms in the following expression: 5a+3b+9c+2a+7b+9c+6+4?

Like terms are: 5a and 2a AND 3b and 7b AND 9c and 9c AND 6 and 4.

TRUE OR FALSE. In 7a+6b+5+4, 5 and 4 are the constant terms.

TRUE.

True or False. In 5a+6b+4c+7, the terms are 5a, 6b, 4c, and 7.

TRUE.

True or False. In 6x+4x+3+2, 6 and 4 are the coefficients.

TRUE.

Which property allows you to write 7+0=7?

The Identity Property of Addition

What are the coefficients of a+b+2?

The coefficient of a is 1 and the coefficient of b is 1.

COEFFICIENT

The coefficient of a term with a variable is the number part of the term. EXAMPLE: In 4x+6x+9, the coefficients are 4 and 6.

Distributive Property

The process of distributing the number outside the parenthesis to each number inside the parenthesis. EXAMPLES: a(b+c)=ab+ac (b+c)a=ba+ca a(b-c)=ab-ac (b-c)a=ba-ca

Associative Property of Multiplication

The product stays the same when the grouping of factors is changed. EXAMPLE: (ab)c=a(bc)

Commutative Property of Multiplication

The product stays the same when the order of the factors is changed. EXAMPLE: ab=ba

Associative Property of Addition

The sum stays the same when the grouping of addends is changed. EXAMPLE: (a+b)+c=a+(b+c)

Commutative Property of Addition

The sum stays the same when the order of the addends is changes. EXAMPLE: a+b=b+a

True or False: 7(9+3)=(7)(9)+(7)(3)

True.