Unit 4, Chapter 4: Expressions and Equations

What is a Coefficient?

A number located before the variable. If there is no variable there is no coefficients

What is a Constant?

A term without a variable. Basically a plain old number.

What are the 4 steps to simply an algebraic expression using Algebra Tiles?

1. Model the expression with Algebra Tiles. 2. Group the "like" tiles together. 3. Eliminate any zero pairs. 4. Write the simplified algebraic expression from the tiles.

Simplify: 4(m + 8n) + n

Distribute: 4m + 32n + n. Reduce like terms further. The final answer is 4m + 33n.

What are Equivalent Expressions?

Expressions that have the same value. Example: 2(x + 3) = 2x + 6 Use a number you choose for x and substitute to check. Using the number 7 for x. 2(7 + 3) = 2(7) + 6 2(10) = 14+6 20 = 20

How do we use the Distributive Property to simply an expression?

Multiply each term inside the parenthesis by the number on the outside of the parenthesis.

What are Like Terms?

Terms with the same variable and the same exponents. Example: 2n

What does it mean to write an expression in its Simplest Form?

That the final expression contains no like terms, no parenthesis. Combine like terms (you may regroup like terms together or highlight, etc...)

What is the Distributive Property?

The Distributive Property is an algebra property which is used to multiply a single term and two or more terms inside a set of parentheses. Examples: a(b + c) = ab+ac a(b - c) = ab-ac

What are the "coefficients" for the following equation: 3n - 5m +6m + 2?

The coefficients are 3, -5, 6.

What are the "coefficients" for the following equation: 3x + 8 + 2x - 1?

The coefficients are 3, 2.

What are the "constants" for the following equation: 3n - 5m +6m + 2?

The constants are 2.

What are the "constants" for the following equation: 3x + 8 + 2x - 1?

The constants are 8, -1.

Simplify: 4 - 2(x - 3y)

The final answer is y - 2x + 6y.

What are the "like terms" for the following equation: 3n - 5m +6m + 2?

The like terms are -5m and 6m.

Simplify: 2m + 3 - 7m - 4.

The like terms are 2m and -7m, The final answer is -5m - 1.

What are the "like terms" for the following equation: 3x + 8 + 2x - 1?

The like terms are 3x and 2x, 8 and -1.

Simplify: 4x + 6 - 3x.

The like terms are 4x and -3x. 6 is left over. The final answer is x + 6.

What are the "terms" for the following equation: 3n - 5m +6m + 2?

The terms are 3n, -5m, 6m, 2.

What are the "terms" for the following equation: 3x + 4y - 5?

The terms are 3x, 4y, -5.

What are the "terms" for the following equation: 3x + 8 + 2x - 1?

The terms are 3x, 8, 2x, -1.

What are Terms?

Things that you add together. Either a number or a product (multiplication) and one or more variables; separated by addition signs. Examples: 8, x, -3x,

True or false. If there is no exponent, you can assume the exponent is one.

True. If there is no exponent, you can assume the exponent is one.

True of false. When we cannot combine the terms inside the parenthesis (because they are not "like terms"), we use the distributive property to eliminate the parenthesis and simplify the expression.

True. When we cannot combine the terms inside the parenthesis (because they are not "like terms"), we use the distributive property to eliminate the parenthesis and simplify the expression. When you can't add or subtract terms because they are not "like terms", you use the Distributive Property to simplify the expressions.