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Simplifying Expressions: Techniques and Examples for Understanding Algebraic Concepts

This section focuses on the essential methods for simplifying algebraic expressions, including how to identify terms and numerical coefficients, recognize like terms, and combine them effectively. Through detailed examples and the application of the distributive property, learners will gain a clear understanding of how to manipulate and simplify expressions. Important cautions are provided to distinguish between terms and factors, ensuring clarity in the simplification process. This is crucial for developing strong algebra skills.

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Simplifying Expressions: Techniques and Examples for Understanding Algebraic Concepts

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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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