# Download PDF by Maud King Murphy: A Beginner's Guide to the Stars

By Maud King Murphy

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E XAM P L E 11 Factoring the Sum of Cubes a. y3 + 125 = y3 + 53 Rewrite 125 as 53. = ( y + 5)(y2 − 5y + 25) b. 3x3 + 192 = 3( x3 + 64) 3 is a common factor. = 3(x3 + 43) Rewrite 64 as 43. = 3(x + 4)(x2 − 4x + 16) Factor. Checkpoint Factor each expression. a. x 3 + 216 b. 5y 3 + 135 Factor. com. Rewrite u6 − v6 as the difference of two squares. Then find a formula for completely factoring u6 − v6. Use your formula to factor completely x6 − 1 and x6 − 64. 3 Polynomials and Factoring Trinomials with Binomial Factors To factor a trinomial of the form ax2 + bx + c, use the following pattern.

186. Writing Explain what is meant when it is said that a polynomial is in factored form. 187. Error Analysis Describe the error. 9x2 − 9x − 54 = (3x + 6)(3x − 9) = 3(x + 2)(x − 3) 188. Think About It Give an example of a polynomial that is prime with respect to the integers. Factoring with Variables in the Exponents In Exercises 189 and 190, factor the expression as completely as possible. 189. x2n − y2n 190. 4 Rational Expressions Domain of an Algebraic Expression The set of real numbers for which an algebraic expression is defined is the domain of the expression.

3 −68 + 4 −5 + √33 √ 86. 1 87. 14 3 88. 5 89. 01 × 106 90. 12 × 10−2 + √15 Using Properties of Radicals In Exercises 91–94, use the properties of radicals to simplify each expression. 4 3 20 3 91. √ ) (−3x)4 3 40x5 √ 93. √12 ∙ √3 94. 3 2 √5x Simplifying a Radical Expression In Exercises 95–102, simplify each expression. 64. 65. √25 × 108 21 800 √ 2 3 32a 95. (a) √45 (b) b2 3 54 (b) 96. (a) √ √32x3y4 3 5 97. (a) √16x (b) √75x2y−4 4 3x4y2 (b) 5 160x8z4 98. (a) √ √ 99. (a) 2√50 + 12√8 (b) 10√32 − 6√18 100.

### A Beginner's Guide to the Stars by Maud King Murphy

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