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How do you expand linear expressions that involve multiplication, addition, and subtraction?

How do you expand linear expressions that involve multiplication, addition, and subtraction?. For example, how do you expand 3(4 + 2x)?. In this lesson you will learn how to expand linear expressions with rational coefficients by using the properties of real numbers. Vocabulary:

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How do you expand linear expressions that involve multiplication, addition, and subtraction?

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  1. How do you expand linear expressions that involve multiplication, addition, and subtraction? For example, how do you expand 3(4 + 2x)?

  2. In this lesson you will learn how to expand linear expressions with rational coefficients by using the properties of real numbers.

  3. Vocabulary: Linear expression Rational coefficient Combine like terms + 2 = 9v 2v + 3 + 7v - 1

  4. Properties of the Real Numbers: Commutative: 11 + 4 = 4 + 11 Associative: (4 + 3) + 9 = 4 + (3 + 9) Distributive: 5(6 + 2) = 5(6) + 5(2)

  5. Failing to distribute negative numbers completely: -9(4 + 3) = -9(4) + 9(3) -

  6. Distributing multiplication over multiplication: 3(5 2) = 3(5) 3(2) - 3(10) 15 6 - = 90 30

  7. Expand 3(2x + 4) + 4 2x 2x + 4 2x + 4 3 2x + 4 + 3(4) = 6x + 12 3(2x) 3(2x + 4) =

  8. Expand and combine like terms: 11(3a- 2) - 6(8a- 9) = 11(3a- 2) + (-6)(8a- 9) = 11(3a) + 11(-2) + (-6)(8a) + (-6)(-9) + (-48a) + 54 + (-22) = 33a + 32 = -15a

  9. In this lesson you have learned how to expand linear expressions with rational coefficients by using the properties of real numbers.

  10. Simplify: 9(5k - 8) - 4(7 - 2k)

  11. Use a diagram to show why 4(3y + 2) = 12y + 8.

  12. Simplify: 5(7y + 1) - 2(9y - 10) + 3(18 - 4y)

  13. Write at least two different linear expressions that expand and simplify to a value of 40x + 27.

  14. 1. Simplify: 7(3x-4) + 2(5 + 6x) 2. Simplify: 11(4 - 8w) - 6(-9w - 5)

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