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Combine Like Terms and Simplify Expressions

Learn how to simplify expressions by combining like terms. Practice identifying terms, coefficients, and constants, and simplify expressions step-by-step.

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Combine Like Terms and Simplify Expressions

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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: 2 + 5x –6x2 + 7x – 3 State the problem. = –6x2 + 5x + 7x – 3 + 2 Group like terms. = –6x2 +12x – 1 Combine like terms.

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

  5. 2q2 + q – 7q – 5q2 3p3 + 5p2–p3 for Example 5 GUIDED PRACTICE SOLUTION 3p3 + 5p2–p3 = 3p3–p3 + 5p2 Group like terms. = 2p3 + 5p3 Combine like terms. SOLUTION 2q2 + q – 7q – 5q2 = 2q2– 5q2– 7q + q Group like terms. = –3q2– 6q Combine like terms.

  6. –4y –x + 10x + y 8(x – 3) – 2(x + 6) for Example 5 GUIDED PRACTICE SOLUTION 8(x – 3) – 2(x + 6) = 8x – 24 – 2x – 12 Distributive property = 8x – 2x – 24 – 12 Group like terms. = 6x – 36 Combine like terms. SOLUTION –4y –x + 10x + y = –4y + y –x + 10x Group like terms. = 9x –3y Combine like terms.

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