Principles of Classical Algebra

May 29th, 2015
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In elementary algebra letters are used to stand for numbers. For example, in the equation ax2+bx+c=0, the letters a, b, and c stand for various known constant numbers called coefficients and the letter x is an unknown variable number whose

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Algebraic Formula:1. (a+ b)2= a2+ 2ab + b22. (a - b)2= a2-2ab + b23. (a + b) (a - b) = a2-b24. (x + a)(x + b) = x2+ (a + b) x + ab5. (x + a)(x - b) = x2+ (a - b) x -ab6. (x - a)(x + b) = x2+ (b - a) x -ab7. (x - a)(x - b) = x2- (a + b) x + ab8. (a + b)3= a3+ b3+ 3ab(a + b)9. (a - b)3= a3- b3- 3ab (a - b)10. (x + y + z)2= x2+ y2+ z2+ 2xy +2yz + 2xz11. (x + y - z)2= x2+ y2+ z2+ 2xy - 2yz - 2xz12. (x - y + z)2= x2+ y2+ z2- 2xy - 2yz + 2xz13. (x - y - z)2= x2+ y2+ z2- 2xy + 2yz - 2xz14. x3+ y3+ z3- 3xyz = (x + y + z)(x2+ y2+ z2- xy - yz -xz)15. x2+ y2=12[(x + y)2+ (x - y)2]16. (x + a) (x + b) (x + c) = x3+ (a + b + c)x2+ (ab + bc + ca)x + abc17. x3+ y3= (x + y) (x2- xy + y2)18. x3- y3= (x - y) (x2+ xy + y2)19. x2+ y2+ z2-xy -yz -zx =12[(x-y)2+(y-z)2+(z-x)2]CBSE Class 9 - Maths - Ch6 - Lines and AnglesUnderstanding Basic Terms.Fill in the Blanks1. A point, a line and a plane are' basic concepts of geometry. These terms are _____ (well defined/undefined).2. A line with two end points is called a _________ (line-segment/ ray).3. A terminated line can be produced ________ (within defined limits/indefinitely).4. A part of a line with one end point is called a _____ (line-segment/ray).5. A line contains ______ (definite/infinite) number of points.6. (One and only one/More than one) _______ line passes t

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