Mathematics

Algebra formulas part-2

Factoring Formulas a2−b2=(a−b)(a+b) a3−b3=(a−b)(a2+ab+b2) a3+b3=(a+b)(a2−ab+b2) a4−b4=(a−b)(a+b)(a2+b2) a5−b5=(a−b)(a4+a3b+a2b2+ab3+b4) Product Formulas (a+b)2=a2+2ab+b2 (a−b)2=a2−2ab+b2 (a+b)3=a3+3a2b+3ab2+b3 (a−b)3=a3−3a2b+3ab2−b3 (a+b)4=a4+4a3b+6a2b2+4ab3+b4 (a−b)4=a4−4a3b+6a2b2−4ab3+b4 (a+b+c)2=a2+b2+c2+2ab+2ac+2bc (a+b+c+...)2=a2+b2+c2+...+2(ab+ac+bc+...)

Set Theory

Definitions: Universal set : I Empty set: ∅ Union of sets A∪B={x:x∈A  or  x∈B} Intersection of sets A∩B={x:x∈A  and  x∈B} Complement A′={x∈I:x∉A} Difference of sets A∖B={x:x∈A  and  x∉B} Cartesian product A×B={(x,y):x∈A  and  y∈B} Set identities involving union...

Algebraic Formulas

a3+b3=(a+b)(a2−ab+b2) a3−b3=(a−b)(a2+ab+b2) a2−b2=(a−b)(a+b) (a−b)2=a2−2ab+b2 (a+b)2=a2+2ab+b2 (a−b)3=a3−3a2b+3ab2−b3 (a+b)3=a3+3a2b+3ab2+b3 x1,2=−b±b2−4ac−−−−−−−√2a a4−b4=(a−b)(a+b)(a2+b2) a5−b5=(a−b)(a4+a3b+a2b2+ab3+b4)

Differentiation Formulas

General Derivative Formulas: 1) Where is any constant. 2) It is called Power Rule of Derivative. 3) 4) Power Rule for Function. 5) 6) 7) 8) 9) It is...

Integration Formulas

1) 2) Where is any constant. 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) or 18) 19) or 20) or 21) 22)...