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ALGEBRA READINESS Chapter 5 Section 6

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**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 Property The 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

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**Identify the property illustrated.**

Example 1 Identifying the Properties of Multiplication Identify the property illustrated. Statement Property Illustrated a. 3 1 x • = Commutative property of multiplication b. 6 5 – ( ) 1 • = Multiplicative property of – 1 Associative property of multiplication c. 2.7 3 – ( ) • x = d. 7 3 – • = Multiplicative property of zero

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**Identify the property illustrated.**

Example 1 Identifying the Properties of Multiplication Identify the property illustrated. Statement Property Illustrated e. 8 1 • = Inverse property of multiplication Identity property of multiplication f. 9.8 • 1 = 4

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Practice for Example 1 Identify the property illustrated. 1. x – • 1 = ANSWER Identity property 2. 3 2 7 5 – • 8 = ANSWER Associative property 3. • = ( ) 21.5 – ANSWER Property of zero

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**Example 2 a. ( ) 5 x – 3.2 = ( ) x 3.2 – 5 = 3.2x – 16 ( ) = 3.2x – 16**

Using the Distributive Property a. ( ) 5 x – 3.2 = ( ) x 3.2 – 5 Distributive property = 3.2x – 16 ( ) Multiply. = 3.2x – 16 + Subtraction rule b. 4 3 – x 2 7 y = 2 7 4 – ( ) x y 3 Distributive property Multiply. – 14y = 4x 3

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Practice for Example 2 Use the distributive property to write an equivalent expression. 3. ( ) 2.4 + x 3 – ANSWER 7.2 3x – 4. ( ) 12y 16x – 4 3 ANSWER 9y 12x + 5. ( ) 2.2 8.7m – 6 ANSWER 13.2 52.2m – 6. w – 2 1 9 ANSWER 19 2w –

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Practice for Example 2 Use the distributive property to write an equivalent expression. 7. ( ) y 7 0.8 – ANSWER 0.8y 5.6 + – 8. ( ) 2 + 3z 0.5 – ANSWER 1 1.5z –

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**Example 3 a. 7x + 5x x = ( ) 5 + 7 = 12x b. 8y 6y + 9 – y = ( ) 8 + 6**

Combining Like Terms a. 7x + 5x x = ( ) 5 + 7 Distributive property = 12x Add. b. 8y 6y + 9 – y = ( ) 8 + 6 9 – Distributive property = 2y 9 + Add.

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**Example 4 3 ( ) x 7 – 4x + = 21 – 3x 4x + = 21 4x + ( ) 3x – x = ( ) 4**

Simplifying Expressions 3 ( ) x 7 – 4x + Distributive property = 21 – 3x 4x + Subtraction rule = 21 4x + ( ) 3x – x = ( ) 4 + 3 – Distributive property 21 Simplify. = 21 + x 10

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**Practice for Examples 3 and 4**

Simplify the expression by combining like terms. 1 3 ANSWER 2 1 r 9. r + r – r 4 4 10. w 1.7w – 3.2w 12.9w ANSWER 15.4w –

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**Practice for Examples 3 and 4**

Simplify the expression. 11. – 5 ( 8x + 2 ) – 3 ANSWER 40x – 13 12. ( ) 10 4r 2 1 r + – ANSWER 3r – 5

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