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Download Algebraic number theory Proc by J. W. S. Cassels, A. Frohlich PDF

By J. W. S. Cassels, A. Frohlich

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Example text

This shortcut will be used throughout the text. For example: 4w ϩ 7w ϭ 11w 8ab2 ϩ 10ab2 Ϫ 5ab2 ϭ 13ab2 3. Simplifying Expressions Clearing parentheses and combining like terms are important tools to simplifying algebraic expressions. This is demonstrated in Example 4. Skill Practice Simplify by clearing parentheses and combining like terms. 11. 7 Ϫ 213x Ϫ 42 Ϫ 5 12. Ϫ16z Ϫ 10y2 Ϫ 413z ϩ y2 Ϫ 8y Example 4 Clearing Parentheses and Combining Like Terms Simplify by clearing parentheses and combining like terms.

10 Ϫ 45 ϩ 2 ϩ 3 Perform multiplication and division from left to right. ϭ Ϫ35 ϩ 2 ϩ 3 Perform addition and subtraction from left to right. ϭ Ϫ33 ϩ 3 ϭ Ϫ30 Answer 26. 2 Example 9 Operations on Real Numbers Apply the Order of Operations Simplify the expression. 0 1Ϫ32 3 ϩ 152 Ϫ 32 0 Ϫ15 Ϭ 1Ϫ32122 Skill Practice Simplify the expression. Ϫ 0 5 Ϫ 7 0 ϩ 11 27. 1Ϫ1 Ϫ 22 2 Solution: 0 1Ϫ32 3 ϩ 152 Ϫ 32 0 Ϫ15 Ϭ 1Ϫ32122 ϭ 0 1Ϫ32 3 ϩ 125 Ϫ 32 0 ϭ 0 1Ϫ32 3 ϩ 1222 0 ϭ 5122 10 0Ϫ27 ϩ 22 0 10 Simplify numerator and denominator separately.

A6x Ϫ 4y ϩ b 4 9 39. 12 40. 32 41. 217c Ϫ 82 Ϫ 516d Ϫ f 2 42. Ϫ21Ϫ3q ϩ r2 Ϫ 715s ϩ 2t2 Objective 3: Simplifying Expressions For Exercises 43–80, clear parentheses and combine like terms. ) 43. 8y Ϫ 2x ϩ y ϩ 5y 44. Ϫ9a ϩ a Ϫ b ϩ 5a 45. 4p2 Ϫ 2p ϩ 3p Ϫ 6 ϩ 2p2 46. 6q Ϫ 9 ϩ 3q2 Ϫ q2 ϩ 10 47. 2p Ϫ 7p2 Ϫ 5p ϩ 6p2 48. 5a2 Ϫ 2a Ϫ 7a2 ϩ 6a ϩ 4 49. m Ϫ 4n3 ϩ 3 ϩ 5n3 Ϫ 9 50. x ϩ 2y3 Ϫ 2x Ϫ 8y3 51. 5ab ϩ 2ab ϩ 8a 52. Ϫ6m2n Ϫ 3mn2 Ϫ 2m2n 53. 14xy2 Ϫ 5y2 ϩ 2xy2 54. 9uv ϩ 3u2 ϩ 5uv ϩ 4u2 55. 81x Ϫ 32 ϩ 1 56.

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