The document discusses applying the distributive property to simplify algebraic expressions. It provides examples of distributing positive and negative coefficients over terms with variables and constants. Key parts of expressions like terms, coefficients, and constant terms are defined. Examples show identifying these parts and simplifying expressions using the distributive property and combining like terms. Practice problems at the end ask the reader to simplify expressions.

1. 2.5 Apply the
Distributive Property

2. Example 1 Apply the distributive property
a. 4( y + 3) = 4y + 12
b. ( y + 7 ) y = y2 + 7y
c. n( n – 9) = n2 – 9n

3. Example 2 Distribute a negative number
Use the distributive property to write an equivalent
expression.
a. – 2( x + 7 ) = – 2( x) + ( – 2 ) ( 7 ) Distribute – 2.
= –2x – 14 Simplify.
b. (5 – y) ( – 3y) = 5( – 3y ) – y ( – 3y ) Distribute – 3y.
= –15y + 3y2 Simplify.
c. – ( 2x – 11) = (–1)( 2x – 11) Multiplicative property of –1
= (–1)( 2x ) – (– 1) ( 11) Distribute – 1.
= – 2x + 11 Simplify.

4. Vocabulary:
• terms: parts of an expression that are
added together
• coefficient: number part of a term with a
variable part
• like terms: have identical variable parts
• constant term: a term that has no variable

5. Example 3 Identify parts of an expression
Identify the terms, like terms, coefficients, and
constant terms of the expression 3x – 4 – 6x + 2.
SOLUTION
Write the expression as a sum: 3x + ( – 4 ) + (– 6x ) + 2
Terms: 3x, – 4, – 6x, 2
Like terms: 3x and – 6x; – 4 and 2
Coefficients: 3, – 6
Constant terms: – 4, 2

6. Example 4 Simplify an expression
Simplify the expression 4( n + 9) – 3( 2 + n).
SOLUTION
4( n + 9) – 3( 2 + n ) = 4n + 36 – 6 – 3n Distributive property
= n + 30 Combine like terms.

7. Guided Practice for Examples 4 and 5
Simplify the expression.
6. 5(6 + n) – 2(n – 2) ANSWER 34 + 3n
7. 4(x – 5) + 3(3 + x) ANSWER 7x – 11