Exercise Simplify. 2(3 • 4).

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Copyright © 2013 Pearson Education, Inc. Section 1.8 Simplifying and Writing Algebraic Expressions.

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Presentation transcript:

Exercise Simplify. 2(3 • 4)

Exercise Simplify. (5 x 3)6

Exercise Simplify. (4 + 10) + 7

Exercise Simplify. 6 + (2 + 11)

Exercise Simplify. x(4 + 10)

Example 1 Simplify. 2(3n) = 6n

Example 2 Simplify. (x + 2) + 9 = x + 11

Constant A constant is a number whose value does not change.

Term A term is a constant, a variable, or the product of a constant and one or more variables. Terms are always separated from each other by a plus or minus sign.

Numerical Coefficient A numerical coefficient is the number factor (constant) accompanying the variable in a term.

3x + 2y − 4

Parts of an Expression 2x3y + 6 2 is the coefficient. x and y are variables. 3 is an exponent. 6 is a constant.

Example 3 Use the −6xy + − z to answer the following. 2 Use the −6xy + − z to answer the following. What are the terms of the equation? −6xy, , and −z x 2

Example 3 Use the −6xy + − z to answer the following. 2 Use the −6xy + − z to answer the following. Does the expression have a constant term? No. All terms contain a variable factor.

Example 3 Use the −6xy + − z to answer the following. 2 Use the −6xy + − z to answer the following. What are the coefficients in the expression? The coefficients are −6, , and −1. 1 2

Like Terms Like terms are terms that have the same variable (or variables) with the same exponents.

Like Terms 5x, −7x, x 1 2 5xy2, −7xy2, 0.75xy2

Unlike Terms 4x, 4x2 6xy, −8xy3

2y + 7y + 3y

Example 4 Simplify. 7x + 4x = (7 + 4)x = 11x

Example 5 Simplify. 2x + 7y + 3 – y + 5x = = (2x + 5x) + (7y – y) + 3

Exercise Simplify. 5r + 8s − 2r + 3s = 3r + 11s

Exercise Simplify. y + 11 − 5y + 4 − 3y = −7y + 15

Exercise Simplify. 6w − 8x − 2w + 3 − 4x = 4w − 12x + 3

Exercise Simplify. −5a + 3z + 2a + 6z = −3a + 9z

Exercise Simplify. 8c + 5y − 2c + 9y = 6c + 14y

Exercise A rectangle has consecutive sides that are represented by x and x+3. Find the expression that represents the perimeter of the rectangle.

Exercise The sides of a triangle are represented by x, 2x, and 2x − 5. Find the expression that represents its perimeter.

Exercise A farmer has a rectangular pasture with dimensions x by 2x. If he places posts 15 ft. apart, how will he represent the distance between each post on the shorter side? on the longer side?

Exercise Each side of a regular octagon (all sides equal in length) is represented by 14x. Find the expression that represents the perimeter of the regular octagon.

Exercise The side of a square is 4 in. shorter than one side of a given rectangle. The side of the rectangle is represented by 2x + 3. Find the expression that represents the perimeter of the square.