TLW use the distributive property to simplify expressions Objective TLW use the distributive property to simplify expressions

The Distributive Property For any numbers a, b, and c, a(b+c) = ab+ac and (b+c)a = ba+ca and a(b−c) = ab−ac and (b−c)a = ba−ca

Examples 3(2 + 5) = 3 • 2 + 3 • 5 3(7) = 6 + 15 21 = 21 √ 4(9 − 7) = 4 • 9 + 4 • 7 4(2) = 36 − 28 8 = 8 √

Notice that it does not matter whether a is placed on the right or the left of the expression in the parentheses. The Symmetric Property of Equality allows the Distributive Property to be written as follows: If a(b + c)=ab + ac, then ab + ac = a(b + c).

The Distributive Property can be used to simplify mental calculations.

You can use algebra tiles to investigate how the Distributive Property relates to algebraic expressions.

You can apply the Distributive Property to algebraic expressions.

A term is a number, a variable, or a product or quotient of numbers and variables. For example, y, p3, and 5g2h are all terms. Like terms are terms that contain the same variables, with corresponding variables having the same power.

2x2 + 6x + 5 Three terms 3a2 + 5a2 + 2a Like terms Unlike terms

The Distributive Property and the properties of equality can be used to show that 5n + 7n = 12n. In this expression, 5n and 7n are like terms. 5n + 7n = (5 + 7)n Distributive Property =12n Substitution

The expressions 5n + 7n and 12n are called equivalent expressions because they denote the same number. An expression is in simplest form when it is replaced by an equivalent expression having no like terms or parentheses.

The coefficient of a term is the numerical factor The coefficient of a term is the numerical factor. For example, in 17xy, the coefficient is 17, and in 3⁄4y2, the coefficient is 3⁄4. In the term m, the coefficient is 1 since 1 • m = m by the Multiplicative Identity Property. Similarly, in the term −m, the coefficient is −1.