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Simplifying Expressions with Like Terms and the Distributive Property

Learn how to simplify algebraic expressions by combining like terms and using the distributive property. Practice examples included.

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Simplifying Expressions with Like Terms and the Distributive Property

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  1. Warm Up Add. 1. 427 + 35 1.80 2. 1.06 + 0.74 462 3. 10 Multiply. 4. 25(8) 5. 1.3(22) 28.6 200 6.

  2. The Distributive Property is used with Addition to Simplify Expressions. The Distributive Property also works with subtraction because subtraction is the same as adding the opposite.

  3. The terms of an expression are the parts to be added or subtracted. Like terms are terms that contain the same variables raised to the same powers. Constants are also like terms. Like terms Constant 4x –3x + 2

  4. A coefficientis a number multiplied by a variable. Like terms can have different coefficients. A variable written without a coefficient has a coefficient of 1. Coefficients 1x2 + 3x

  5. Using the Distributive Property can help you combine like terms. You can factor out the common factors to simplify the expression. 7x2 – 4x2 = (7 – 4)x2 Factor out x2 from both terms. = (3)x2 Perform operations in parenthesis. = 3x2 Notice that you can combine like terms by adding or subtracting the coefficients and keeping the variables and exponents the same.

  6. Example 3A: Combining Like Terms Simplify the expression by combining like terms. 72p – 25p 72p –25p 72p and 25p are like terms. 47p Subtract the coefficients.

  7. and are like terms. Write 1 as . Example 3B: Combining Like Terms Simplify the expression by combining like terms. A variable without a coefficient has a coefficient of 1. Add the coefficients.

  8. Example 3C: Combining Like Terms Simplify the expression by combining like terms. 0.5m + 2.5n 0.5m + 2.5n 0.5m and 2.5n are not like terms. 0.5m + 2.5n Do not combine the terms.

  9. 3m2 + m3 Check It Out! Example 3 Simplify by combining like terms. 3a. 16p + 84p 16p + 84p 16p + 84p are like terms. 100p Add the coefficients. 3b. –20t – 8.5t2 –20t – 8.5t2 20t and 8.5t2 are not like terms. –20t – 8.5t2 Do not combine the terms. 3c. 3m2 + m3 3m2 + m3 3m2 and m3are not like terms. Do not combine the terms.

  10. Example 4: Simplifying Algebraic Expressions Simplify 14x + 4(2 + x). Justify each step. Procedure Justification 1. 14x + 4(2 + x) 2. 14x + 4(2) + 4(x) Distributive Property 3. 14x + 8 + 4x Multiply. Commutative Property 4. 14x + 4x + 8 5. (14x + 4x) + 8 Associative Property 6. 18x + 8 Combine like terms.

  11. Check It Out! Example 4a Simplify 6(x –4) + 9.Justify each step. Procedure Justification 1. 6(x –4) + 9 2. Distributive Property 6(x)–6(4) + 9 3. 6x – 24 + 9 Multiply. Combine like terms. 4. 6x – 15

  12. Check It Out! Example 4b Simplify −12x – 5x + 3a + x.Justify each step. Procedure Justification 1. –12x – 5x + 3a + x 2. Commutative Property –12x – 5x + x + 3a 3. –16x + 3a Combine like terms.

  13. Lesson Quiz: Part II Simplify each expression by combining like terms. Justify each step with an operation or property. 5. 14c2 – 9c 6. 14c2 – 9c 7. 301x – x 300x 8. 24a + b2 + 3a + 2b2 27a + 3b2

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