VOCAB Term- A number, variable, or the product or quotient of a number and one or more variables. Assessment Questions Assessment Questions Assessment Questions The Distributive Property Constant- A term that has no variable factor Coefficient- The numerical factor when a term has a variable. Like Terms- Terms with exactly the same variable factors in a variable expression. The Distributive Property An algebra property which is used to multiply a single term and two or more terms inside a set of parentheses. Simplifying an Expression

EXAMPLE 2(5x + 3)

2(5x + 3) = 2(5x) + 2(3)

= 10x + 6 (3b - 2)(1/3)

(3b - 2)(1/3) = 3b(1/3) - 2(1/3)

= b - 2/3 Explanation Using the Distributive Property of -1

EXAMPLE Simplify: -(6x + 4)

-(6x + 4)= -1(6x + 4)

= -1(6x) +(-1)(4)

= -6x - 4

-(2x + 1)

-(2x + 1)= -1(2x + 1)

= -1(2x) + (-1)(1)

= -2x - 1 Explanation When you see a distributive property problem, it usually has a number outside the parenthesis, but in this part of the distributive property it is a -1 or just a negative sign that represents -1. You still do the same thing; you multiply -1 by everything inside the parenthesis. Then solve. Combining Like Terms

EXAMPLE Explanation When you are combining like terms, there is usually more than one variable and number. First you look for the variables.

12r+5+3r-5

Now you add them.

12r+5+3r-5

15r

Then you look for the numbers.

12r+5+3r-5

0

Now whatever you have left is the answer. Make sure to double check your work. In a problem that is solved by the Distributive property, there are numbers inside of the parenthesis and a number on the outside. What you do is you take the number on the outside and you multiply it by every number on the inside. Once you multiply, you are left with a simple equation that you solve and the answer is the answer overall. (example shown above) n-10+9n-3 10n -13 -5n+3(6+7n) +18+21n 16n+18 Question #1 Question #2 Assessment Question Match each vocab. word with its definition ____. Term

____. Constant

____. Coefficient

____. Like Terms A.The numerical factor when a

term has a variable.

B. Terms with exactly the same

variable factors in a variable

expression.

C. A term that has a variable

factor.

D. A number or variable, or the

product of a number & one or

more variables.

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# The Distributive Property

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