Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Location arithmetic wikipedia , lookup
Bra–ket notation wikipedia , lookup
Real number wikipedia , lookup
Mathematics of radio engineering wikipedia , lookup
Laws of Form wikipedia , lookup
Elementary mathematics wikipedia , lookup
Non-standard calculus wikipedia , lookup
Fundamental theorem of algebra wikipedia , lookup
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. Let’s Review Let’s Review Vocabulary: Linear expression Rational coefficient Combine like terms 2v + 3 + 7v - 1 = 9v + 2 Let’s Review Let’s Review 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) A Common Let’s Review Mistake Failing to distribute negative numbers completely: -9(4 + 3) = -9(4) + 9(3) A Common Let’s Review Mistake Distributing multiplication over multiplication: 3(5 2) = 3(5) 3(2) 3(10) 30 = 15 6 90 CoreReview Lesson Let’s Expand 3(2x + 4) 2x 3 3(2x + 4) = x x x + x x x 3(2x) 4 1 1 1 1 1 1 1 1 2x + 4 2x + 4 1 1 1 1 2x + 4 + 3(4) = 6x + 12 CoreReview Lesson Let’s 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) = 33a + (-22) + (-48a) + 54 = -15a + 32 In this lesson you have learned how to expand linear expressions with rational coefficients by using the properties of real numbers. Guided Practice Let’s Review Simplify: 9(5k - 8) - 4(7 - 2k) Extension Let’s ReviewActivities Use a diagram to show why 4(3y + 2) = 12y + 8. Extension Let’s ReviewActivities Simplify: 5(7y + 1) - 2(9y - 10) + 3(18 - 4y) Extension Let’s ReviewActivities Write at least two different linear expressions that expand and simplify to a value of 40x + 27. Quick Quiz Let’s Review 1. Simplify: 7(3x-4) + 2(5 + 6x) 2. Simplify: 11(4 - 8w) - 6(-9w - 5)