2 5.6: Use the Distributive Property The parts of an expression that are added together are the terms of the expression.A term that has no variable part is a constant term.The number part of a variable part is called the coefficient of the term.Like terms have the same variable raised to the same power.You can combine like terms by adding the coefficients of the terms.Distributive PropertyThe product of a number and the sum (or difference) of two other numbers is equal to the sum (or difference) of the products of the number and each other.a(b + c) = ab + ac a(b – c) = ab – ac
3 Identify the property illustrated. Example 1Identifying the Properties of MultiplicationIdentify the property illustrated.StatementProperty Illustrateda.31x•=Commutative property of multiplicationb.65–()1•=Multiplicative property of – 1Associative property of multiplicationc.2.73–()•x=d.73–•=Multiplicative property of zero
4 Identify the property illustrated. Example 1Identifying the Properties of MultiplicationIdentify the property illustrated.StatementProperty Illustratede.81•=Inverse property of multiplicationIdentity property of multiplicationf.9.8•1=4
5 Practice for Example 1Identify the property illustrated.1.x–•1=ANSWERIdentity property2.3275–•8=ANSWERAssociative property3.•=()21.5–ANSWERProperty of zero
6 Example 2 a. ( ) 5 x – 3.2 = ( ) x 3.2 – 5 = 3.2x – 16 ( ) = 3.2x – 16 Using the Distributive Propertya.()5x–3.2=()x3.2–5Distributive property=3.2x–16()Multiply.=3.2x–16+Subtraction ruleb.43–x27y=274–()xy3Distributive propertyMultiply.–14y=4x3
7 Practice for Example 2Use the distributive property to write an equivalent expression.3.()2.4+x3–ANSWER7.23x–4.()12y16x–43ANSWER9y12x+5.()2.28.7m–6ANSWER13.252.2m–6.w–219ANSWER192w–
8 Practice for Example 2Use the distributive property to write an equivalent expression.7.()y70.8–ANSWER0.8y5.6+–8.()2+3z0.5–ANSWER11.5z–
9 Example 3 a. 7x + 5x x = ( ) 5 + 7 = 12x b. 8y 6y + 9 – y = ( ) 8 + 6 Combining Like Termsa.7x+5xx=()5+7Distributive property=12xAdd.b.8y6y+9–y=()8+69–Distributive property=2y9+Add.