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Introduction to Algebra, , 1. In algebra, we substitute number with letters or alphabets to arrive at, a solution., , 2. We use letters like x,m,a,b,etc. to represent unknown quantities in the, equation., , Important Algebraic Formulae, , 1. (a+ b)? =a? + 2ab + b?, , 2. (a- b)? = a? - 2ab + b?, , 3. a?- b?=(a+b)(a-b), , 4. a? + b?=(a+b)?- 2ab, , =(a-b)?+2ab, 5. (a + b)? = a? + 3a’b + 3ab? + b*, , 6. (a - b)? = a? - 3a*b + 3ab? - b?, 7. a? + b? = (a + b) (a? - ab + b?), 8. a - b? = (a - b) (a? + ab + b?), 9. (a+ b)?-(a-b)?=4ab, 10. (a+ b+c)?=a?+b?+c? + 2ab + 2be + 2ac, 11. a? +b? +c? - 3abc = (a+ b + c)(a? + b? + c? - ab - bc- ac), 12.ifa+b+c=0 then a®?+b*+c?=3abc, 13. a*+a?+1=(a?+a+1) (a?-a+1), 14. a* + a*b? + b* = (a? + ab + b?) (a? - ab + b?), 15. a* - b* = (a? + b?) (a + b)(a - b), 16. a® - b® = (a*+ b*) (a? + b?)(a + b)(a - b), 17.a"xa"=a™"", 18,2 =a", , a, 19. (a™)"=a™, , 20. (ab)* = a*b”, , 21.(2}= =, 22. at= Xa