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Note Taking Guide 1.2

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1.02 Algebraic Expressions Essential Questions After completing this lesson, you will be able to answer the following questions: How do you interpret expressions that represent a quantity in terms of its context? How do you interpret parts of an expression, such as terms, factors, and coefficients? How do you interpret and simplify complicated expressions by viewing one or more of their parts as a single entity? Main Idea (page #) DEFINITION OR SUMMARY EXAMPLE Algebraic Expressions(P.1) An algebraic expression is an expression that contains one or more numbers, one or more variables, and one or more arithmetic operations. There are 4 boxes of video games. If each box contains x number of games: 4x Vocabulary(P.2): Like __________: have identical variable parts

Factoring Polynomials of Degree 3

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Factoring Polynomials of Degree 3 Factoring a 3 - b 3 An expression of the form a 3 - b 3 is called a difference of cubes. The factored form of a 3 - b 3 is (a - b)(a 2 + ab + b 2) : (a - b)(a 2 + ab + b 2) = a 3 - a 2 b + a 2 b - ab 2 + ab 2 - b 3 = a 3 - b 3 For example, the factored form of 27x 3 - 8 ( a = 3x, b = 2 ) is (3x - 2)(9x 2 + 6x + 4) . Similarly, the factored form of 125x 3 -27y 3 ( a = 5x, b = 3y ) is (5x - 3y)(25x 2 +15xy + 9y 2) . To factor a difference of cubes, find a and b and plug them into (a - b)(a 2 + ab + b 2) . Factoring a 3 + b 3 An expression of the form a 3 + b 3 is called a sum of cubes. The factored form of a 3 + b 3 is (a + b)(a 2 - ab + b 2) : (a + b)(a 2 - ab + b 2) = a 3 + a 2 b - a 2 b - ab 2 + ab 2 + b 3 = a 3 - b 3 .
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