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Comprehensive Guide to Algebra: Formulae, Factoring, and Properties of Inequalities

This study presentation covers fundamental algebra concepts including common formulae, factoring techniques, and solving equations. Key topics explored include the difference of squares, perfect square trinomials, properties of inequalities, and exponent rules. It also discusses various properties of radicals and arithmetic operations in detail. Whether you're preparing for exams or simply looking to strengthen your algebra skills, this resource provides clear explanations and examples for each topic.

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Comprehensive Guide to Algebra: Formulae, Factoring, and Properties of Inequalities

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  1. Study Pages Study Presentation on Algebra Formulae & such

  2. Factoring and Solving

  3. x2– a2 = (x+a)(x-a)

  4. x2+ 2ax+ a2 = (x+a)2

  5. (x + a)2= x2+2ax+ a2

  6. x2- 2ax + a2 = (x-a)2

  7. (x-a)2= x2- 2ax + a2

  8. Arithmetic Operations

  9. abc a . bc

  10. abc ac . b

  11. Properties of Inequalities

  12. (adding or subtracting c)If a < b then: a+c<b+canda-c < b-c

  13. (multiplying or dividing by c)If a < b ANDc > 0 then: ac <bcanda/c < b/c

  14. (multiplying or dividing by c)If a < b ANDc < 0 then: ac >bcanda/c > b/c

  15. Exponent Properties

  16. (ab)n = anbn

  17. (an)m = anm

  18. anam = an+m

  19. an/m = (a1/n)m = (a1/m)n

  20. a-n = 1 an

  21. a0 = 1 a ≠ 0

  22. (a/b)-n = (b/a)n =bnan

  23. an/am = an-m =1/am-n

  24. (a/b)n = = anbn

  25. Properties of Radicals

  26. ⁿ√a = a1/n

  27. ⁿ√ab = ⁿ√a(ⁿ√b)

  28. ⁿ√aⁿ = |a|

  29. m√ⁿ√a = nm√a

  30. na/b = n√a n√b

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