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For Exercises 65–70, multiply or divide as indicated. (See Example 7.)
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Beginning and Intermediate Algebra
- In Exercises 106–108, factor and simplify each algebraic expression. 106. 16x + 32r4 107. (x² – 4)(x² + 3) - (r? – 4)°(x² + 3)2 108. 12x+ 6xarrow_forwardIn Exercises 129–132, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. 129. 9x? + 15x + 25 = (3x + 5) 130. x - 27 = (x – 3)(x² + 6x + 9) 131. x³ – 64 = (x – 4)3 132. 4x2 – 121 = (2x – 11)arrow_forwardIn Exercises 14–16, divide as indicated. 14. (12x*y³ + 16x?y³ – 10x²y²) ÷ (4x?y) 15. (9x – 3x2 – 3x + 4) ÷ (3x + 2) 16. (3x4 + 2x3 – 8x + 6) ÷ (x² – 1)arrow_forward
- For Exercises 37–44, find the difference quotient and simplify. (See Examples 4-5) 37. f(х) — — 2х + 5 38. f(x) = -3x + 8 39. f(x) = -5x² – 4x + 2 40. f(x) = -4x - 2x + 6 41. f(x) = x' + 5 42. f(x) = 1 43. f(x) = 1 44. f(x) = x + 2arrow_forwardFor Exercises 19–26, simplify each expression and write the result in standard form, a + bi. 8 + 3i 19. 4 + 5i 20. -4 - 6i 21. 9 - 15i 22. 14 6. -2 -3 -18 + V-48 23. - 20 + V-50 14 - V-98 25. - 10 + V-125 24. 26. 4 10 -7arrow_forwardRationalize the numerator of x+10 – 100 Paragraph A.arrow_forward
- For Exercises 81–100, make an appropriate substitution and solve the equation. (See Examples 10–11) 81. (2x + 5)? – 7(2x + 5) - 30 = 0 82. (Зх — 7)? - 6(3х — 7)-16 3D 0 83. (x + 2x)? – 18(r + 2x) = -45 84. (x + 3x)? - 86. (у? — 3)? — 9(y? — 3) — 52 %3D 0 14(x + 3x) = -40 85. (x + 2)2 + (x + 2) – 42 = 0 10 2 10 - 61 m - - 27 = 0 x + + 35 = 0 87. 88. - 121 x + т - m m 89. 2 + 2 + = 12 90. + 3 + 6 + 3 = -8 91. 5c2/5 11c/5 + 2 = 0 92. З3 d'/3 – 4 = 0 93. y'/2 – y/4 6 = 0 94. n'/2 + 6n/4 – 16 = 0 95. 9y 10y + 1 = 0 96. 100х-4 29x-2 + 1 = 0 | 97. 4t – 25 Vi = 0 98. 9m – 16Vm = 0 100. 392 + 16q -1 99. 30k-2 – 23k- + 2 = 0 + 5 = 0arrow_forwardVerify that A(B+C) = AB+ACarrow_forwardverify that A(B + C) = AB + ACarrow_forward
- For Exercises 7–18, write each expression in terms of i and simplify. (See Example 1) 7. V-121 8. V-100 9. V-98 10. V-63 11. V-4V-9 12. V-IV-36 13. V-10V=5 14. V-6V-15 V-98 15. V-2 V-45 16. V-5 V-63 17. V-80 18. V5 Vīarrow_forwardFor Exercises 73–80, (a) evaluate the discriminant and (b) determine the number and type of solutions to each equation. (See Example 9) 73. Зх? 4х + 6 3D 0 74. 5x - 2x + 4 = 0 75. - 2w? + 8w = 3 76. -6d + 9d = 2 77. Зx(х — 4) 3D х — 4 78. 2x(x – 2) = x + 3 79. –1.4m + 0.1 = -4.9m² 80. 3.6n + 0.4 = -8.1n?arrow_forwardIn Exercises 20–21, solve each rational equation. 11 20. x + 4 + 2 x2 – 16 - x + 1 21. x? + 2x – 3 1 1 x + 3 x - 1 ||arrow_forward
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