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# 002 review of algebra

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### 002 review of algebra

1. 1. Review of Basic Algebra:<br /><ul><li>The denominator of a fraction can never equal to zero.
2. 2. 04 is zero, but 40 is undefined
3. 3. The reciprocal of a number or expression is its multiplicative inverse.
4. 4. The reciprocal of 43 is 34
5. 5. The reciprocal of 6 is 16
6. 6. The reciprocal of x+1 is 1x+1
7. 7. Multiply fractions
8. 8. 23 x 52=106 = 53
9. 9. Dividing fractions
10. 10. 23 ÷ 52
11. 11. =23 x 25=415
13. 13. 23+ 53=2 + 53=73
14. 14. 25+ 58=16 + 2540=4140
15. 15.
16. 16. Subtracting fractions
18. 18. Substitution
19. 19. An algebraic expression or just expression is something like xyz or a3p2q-6, basically without equal sign (if it has an equal sign, it is an equation).
20. 20. If we substitute x = (a + b) to x2yz we will have (a+b)2yz
21. 21. Canceling fractions
22. 22. x5y2x3yz=x2yz
23. 23. You can cancel fractions only when it has unbroken chain or multiplication through the entire numerator and the entire denominator.
24. 24. a2b2xy-pq4(c+d)ab4z(xy-pq)3=axy-pq(c+d)b2z
25. 25. Absolute Value
26. 26. Absolute value just turns the negative number into a positive number and does nothing to a positive number or zero.
27. 27. |-6| = 6
28. 28. Powers</li></ul> xo= 1<br /><ul><li> x-3=1x3 </li></ul>x2∙x3=x5<br />x6x3=x3<br /> x32=x6<br /> xyz3=x3y3z3<br /> yx3=y3x3<br /><ul><li>Radicals
29. 29. 3x2=x23
30. 30.
31. 31. Factoring
32. 32. Difference of two squares: a2-b2=a+b(a-b)
33. 33. Sum of two cubes: a3+b3=a+b(a2-ab+b2)
34. 34. Difference of two cubes: a3-b3=a-b(a2+ab+b2)
35. 35. Factoring a polynomial: x2+x-2=x+2(x-1)</li></ul>Seatwork: Simplify the following<br /><ul><li>8x2-11-5x+2x2+4
36. 36. x-x3-x2+9(2x2-7x-8)
37. 37. 1x-y+3x+yx2-y2
38. 38. 4x-7-3x+7
39. 39. 5x32-16-34-x</li></ul>Assignment: Simplify the following<br /><ul><li>2x-8x-y-3-(x+4y+3x]
40. 40. 3x2-5x-2(x2-4x+3)
41. 41. 4x-7+2x49-x2
42. 42. 6x4-x-24+x
43. 43. x-1 - 2x+2 x + 2 - 2x-1</li></ul>Reference: Calculus for Dummies by Mark Ryan © Wiley Pub., 2003<br />