1. Ch 2 Sec 2B: Slide #1 Columbus State Community College Chapter 2 Section 2B Simplifying Expressions

2. Ch 2 Sec 2B: Slide #2 Simplifying Expressions 1.Simplify expressions. 2.Identify terms and numerical coefficients. 3.Identify like terms. 4.Combine like terms.

3. Ch 2 Sec 2B: Slide #3 Simplifying Expressions EXAMPLE 1 Simplifying Expressions (a)6 ( 3x – 7y ) Simplify each expression. Use the distributive property. 6 ( 3x – 7y )= 6 ( 3x )– 6 ( 7y ) = 18x – 42y

4. Ch 2 Sec 2B: Slide #4 Simplifying Expressions EXAMPLE 1 Simplifying Expressions (b)24 – ( 5x – 3 ) Simplify each expression. –x = –1 x24 – 1 ( 5x – 3 ) = 24 – 5x + 3 1 = 27 – 5x or –5x + 27 Distributive property Add.

5. Ch 2 Sec 2B: Slide #5 CAUTION It is important to be able to distinguish between terms and factors. For example, in the expression 5x 3 + 4x 3, there are two terms, 5x 3 and 4x 3. Terms are separated by a + or – sign. On the other hand, in the one-term expression ( 5x 3 )( 4x 3 ), 5x 3 and 4x 3 are factors. Factors are multiplied.

6. Ch 2 Sec 2B: Slide #6 CAUTION Remember that only like terms may be combined.

7. Ch 2 Sec 2B: Slide #7 Simplifying Expressions Involving Like Terms EXAMPLE 2 Simplifying Expressions Involving Like Terms (a)7n + 4 ( 9 + 2n ) Simplify each expression. Distributive property= 7n + 4 ( 9 ) + 4 ( 2n ) (a)7n + 4 ( 9 + 2n ) Multiply.= 7n + 36 + 8n Combine like terms.= 15n + 36

8. Ch 2 Sec 2B: Slide #8 (b)12c + 7 – 2 ( c – 6 ) Simplifying Expressions Involving Like Terms EXAMPLE 2 Simplifying Expressions Involving Like Terms Simplify each expression. Distributive property= 12c + 7 – 2 ( c ) – 2 ( – 6 ) Multiply.= 12c + 7 – 2c + 12 Combine like terms.= 10c + 19

9. Ch 2 Sec 2B: Slide #9 (c)– ( 5 – m ) – 7m Simplifying Expressions Involving Like Terms EXAMPLE 2 Simplifying Expressions Involving Like Terms Simplify each expression. – ( 5 – m ) = – 1 ( 5 – m )= – 1 ( 5 – m ) – 7m Distribute.= – 1 ( 5 ) – 1 ( – m ) – 7m Multiply.= –5 + m – 7m Combine like terms.= –5 – 6m

10. Ch 2 Sec 2B: Slide #10 (d)6 ( 3n 2 – 4 ) – 4 ( 5n 2 – 7 ) Simplifying Expressions Involving Like Terms EXAMPLE 2 Simplifying Expressions Involving Like Terms Simplify each expression. Distribute.= 6 ( 3n 2 ) – 6 ( 4 ) – 4 ( 5n 2 ) – 4 ( –7 ) Multiply.= 18n 2 – 24 – 20n 2 + 28 Combine like terms.= –2n 2 + 4

11. Ch 2 Sec 2B: Slide #11 Simplifying Expressions Chapter 2 Section 2B – Completed Written by John T. Wallace