Changes
From Karnataka Open Educational Resources
1,140 bytes added
, 11:34, 4 November 2019
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| =Algebraic Identities= | | =Algebraic Identities= |
| + | *<math>(a+b)(a-b)=a^2-b^2</math> |
| + | *<math>(a+b)^2=a^2+2ab+b^2</math> |
| + | *<math>(a-b)^2=a^2-2ab+b^2</math> |
| + | *<math>(x+a)(x+b)=x^2+x(a+b)+ab</math> |
| + | *<math>(x+a)(x+b)(x+c)=x^3+x^2(a+b+c)+x(ab+bc+ca)+abc</math> |
| + | *<math>(a+b)^3=a^3+3ab(a+b)+b^3</math> |
| + | *<math>(a-b)^3=a^3-3ab(a-b)-b^3</math> |
| + | *<math>a^3+b^3=(a+b)(a^2-ab+b^2)</math> |
| + | *<math>a^3-b^3=(a-b)(a^2+ab+b^2)</math> |
| + | *<math>(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca</math> |
| + | *<math>a^4+a^2b^2+b^4=(a^2+b^2+ab)(a^2+b^2-ab)</math> |
| + | *<math>(a+b+c)^3-a^3-b^3-c^3=3(a+b)(b+c)(c+a)</math> |
| + | *<math>(a+b)(b+c)(c+a)=(a+b+c)(ab+bc+ca)-abc</math><br> |
| + | |
| + | |
| =Geometric Results= | | =Geometric Results= |
| + | |
| =Formulae for commercial arithmetic= | | =Formulae for commercial arithmetic= |
| =Statistical Formulae= | | =Statistical Formulae= |
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| |- | | |- |
| |Triangle | | |Triangle |
− | |
| |
| |(a+b+c), where a, b, c are sides | | |(a+b+c), where a, b, c are sides |
| |<math>\frac{1}{2}bh</math> | | |<math>\frac{1}{2}bh</math> |
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| |<math>2(l+b)</math> | | |<math>2(l+b)</math> |
| Where l & b are the length & breadth | | Where l & b are the length & breadth |
− | |<math>lxb</math> | + | |<math>lb</math> |
| + | |- |
| + | |Trapezium |
| + | |<math>(a+b+c+d)</math> |
| + | Where a,b,c and d are the sides |
| + | |<math>\frac{1}{2}h(a+b)</math> |
| + | Where a and b are parallel sides of trapezium. And h is the perpendicular distance between two parallel sides. |
| + | |- |
| + | |Parallelogram |
| + | |<math>2(a+b)</math> |
| + | Where a & b are the sides of Parallelogram |
| + | |<math>bh</math> |
| + | Where b is base and h is the perpendicular distance between base b and its parallel side. |
| + | |- |
| + | |Rhombus |
| + | |<math>4a</math> |
| + | Where a is the side of a rhombus |
| + | |<math>\frac{1}{2}(d_{1}d_{2})</math> |
| + | Where d1 and d2 are diagonals of rhombus |
| |- | | |- |
| |} | | |} |
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| |- | | |- |
| |} | | |} |
| + | |
| + | [[Category:Mathematics]] |