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Columbus State Community College

Columbus State Community College. Chapter 2 Section 2B Simplifying Expressions. Simplifying Expressions. Simplify expressions. Identify terms and numerical coefficients. Identify like terms. Combine like terms. Simplifying Expressions. EXAMPLE 1 Simplifying Expressions.

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Columbus State Community College

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  1. Columbus State Community College Chapter 2 Section 2B Simplifying Expressions

  2. Simplifying Expressions • Simplify expressions. • Identify terms and numerical coefficients. • Identify like terms. • Combine like terms.

  3. Simplifying Expressions EXAMPLE 1 Simplifying Expressions Simplify each expression. (a) 6 ( 3x – 7y ) Use the distributive property. 6 ( 3x – 7y ) = 6 ( 3x ) – 6 ( 7y ) = 18x– 42y

  4. Simplifying Expressions EXAMPLE 1 Simplifying Expressions Simplify each expression. (b) 24 – ( 5x – 3 ) 24 – 1 ( 5x – 3 ) 1 –x = –1 • x = 24 – 5x + 3 Distributive property = 27 – 5xor –5x + 27 Add.

  5. CAUTION CAUTION It is important to be able to distinguish between terms and factors. For example, in the expression 5x3 + 4x3, there are two terms, 5x3and 4x3. Terms are separated by a + or – sign. On the other hand, in the one-term expression ( 5x3 )( 4x3), 5x3and 4x3are factors. Factors are multiplied.

  6. CAUTION CAUTION Remember that only like terms may be combined.

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

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

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

  10. Simplifying Expressions Involving Like Terms EXAMPLE 2 Simplifying Expressions Involving Like Terms Simplify each expression. (d) 6 ( 3n2 – 4 ) – 4 ( 5n2 – 7 ) (d)6 ( 3n2 – 4 ) –4 ( 5n2 – 7 ) = 6 ( 3n2 ) – 6 ( 4 ) – 4 ( 5n2 ) – 4 ( –7 ) Distribute. = 18n2 – 24 – 20n2 + 28 Multiply. = –2n2 + 4 Combine like terms.

  11. Simplifying Expressions Chapter 2 Section 2B – Completed Written by John T. Wallace

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