5 ( ) Check It Out! Example 1c Simplify. 1 2 7 • 8 1 2 8 • 7 Use the Commutative Property.()12•87Use the Associative Property to make groups of compatible numbers.4•728
6 The Distributive Property is used with Addition to Simplify Expressions. The Distributive Property also works with subtraction because subtraction is the same as adding the opposite.
7 The terms of an expression are the parts to be added or subtracted The terms of an expression are the parts to be added or subtracted. Like terms are terms that contain the same variables raised to the same powers. Constants are also like terms.Like termsConstant4x – 3x + 2
8 A coefficient is a number multiplied by a variable A coefficient is a number multiplied by a variable. Like terms can have different coefficients. A variable written without a coefficient has a coefficient of 1.Coefficients1x2 + 3x
9 Using the Distributive Property can help you combine like terms Using the Distributive Property can help you combine like terms. You can factor out the common factors to simplify the expression.7x2 – 4x2 = (7 – 4)x2Factor out x2 from both terms.= (3)x2Perform operations in parenthesis.= 3x2Notice that you can combine like terms by adding or subtracting the coefficients and keeping the variables and exponents the same.
10 Example 3A: Combining Like Terms Simplify the expression by combining like terms.72p – 25p72p – 25p72p and 25p are like terms.47pSubtract the coefficients.
11 Example 3C: Combining Like Terms Simplify the expression by combining like terms.0.5m + 2.5n0.5m + 2.5n0.5m and 2.5n are not like terms.0.5m + 2.5nDo not combine the terms.
12 Check It Out! Example 3Simplify by combining like terms.3a. 16p + 84p16p + 84p16p + 84p are like terms.100pAdd the coefficients.3b. –20t – 8.5t2–20t – 8.5t220t and 8.5t2 are not like terms.–20t – 8.5t2Do not combine the terms.3c. 3m2 + m33m2 + m33m2 and m3 are not like terms.3m2 + m3Do not combine the terms.