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Simplifying Expressions: Combining Like Terms and Applying the Distributive Property

In this guide, we will simplify mathematical expressions by combining like terms, identifying coefficients, and utilizing the distributive property. We provide step-by-step examples demonstrating how to group and combine terms effectively. We'll explore various expressions and crucial concepts like terms, constants, and like terms, ensuring a solid understanding of simplification techniques. Practice problems and guided solutions will reinforce your learning and help you confidently tackle similar problems in algebra.

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Simplifying Expressions: Combining Like Terms and Applying the Distributive Property

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  1. 8x + 3x 5p2 + p – 2p2 3(y + 2) – 4(y – 7) EXAMPLE 4 Simplify by combining like terms = (8 + 3)x Distributive property = 11x Add coefficients. = (5p2– 2p2) + p Group like terms. = 3p2 + p Combine like terms. = 3y + 6 – 4y + 28 Distributive property = (3y – 4y) + (6 + 28) Group like terms. = –y + 34 Combine like terms.

  2. 2x – 3y – 9x + y EXAMPLE 4 Simplify by combining like terms = (2x – 9x) + (– 3y + y) Group like terms. = –7x – 2y Combine like terms.

  3. for Example 5 GUIDED PRACTICE 8. Identify the terms, coefficients, like terms, and constant terms in the expression 2 + 5x – 6x2 + 7x – 3. Then simplify the expression. SOLUTION Terms: 2, 5x, –6x2 , 7x, –3 5 from 5x, –6 from –6x2 , 7 from 7x Coefficients: Like terms: 5xand 7x, 2 and –3 Constants: 2 and –3 Simplify: –6x2 +12x – 1

  4. 15m – 9m 2n – 1 + 6n + 5 for Example 5 GUIDED PRACTICE Simplify the expression. SOLUTION 6m SOLUTION 8n + 4

  5. 2q2 + q – 7q – 5q2 3p3 + 5p2–p3 for Example 5 GUIDED PRACTICE SOLUTION 2p3 + 5p2 SOLUTION –3q2– 6q

  6. –4y –x + 10x + y 8(x – 3) – 2(x + 6) for Example 5 GUIDED PRACTICE SOLUTION 6x – 36 SOLUTION 9x –3y

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