ALGEBRA (बीजगणित),iti 2nd Year ke student ke liye, जिन्हें algebra शुरुआत से पढ़ना हैं जरुर देखे

Описание: ALGEBRA (बीजगणित),iti 2nd Year ke student ke liye, जिन्हें algebra शुरुआत से पढ़ना हैं जरुर देखे
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ALGEBRA (बीजगणित),iti 2nd Year ke student ke liye, जिन्हें algebra शुरुआत से पढ़ना हैं जरुर देखे
Algebra formulas are rules or identities that simplify expressions and solve equations, with key examples including binomial squares like \((a+b)^{2}=a^{2}+2ab+b^{2}\), difference of squares \(a^{2}-b^{2}=(a-b)(a+b)\), and the quadratic formula \(x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}\) for \(ax^{2}+bx+c=0\), alongside laws of exponents such as \((a^{m})(a^{n})=a^{m+n}\) and formulas for factoring sums/differences of cubes like \(a^{3}+b^{3}=(a+b)(a^{2}-ab+b^{2})\). These expressions use variables (letters) and constants to show relationships in mathematics. Common Algebraic Identities (Binomials) Square of a Sum: \((a+b)^{2}=a^{2}+2ab+b^{2}\)Square of a Difference: \((a-b)^{2}=a^{2}-2ab+b^{2}\)Difference of Squares: \(a^{2}-b^{2}=(a-b)(a+b)\)Square of a Trinomial: \((a+b+c)^{2}=a^{2}+b^{2}+c^{2}+2ab+2bc+2ca\) Formulas for Cubes & Factoring Sum of Cubes: \(a^{3}+b^{3}=(a+b)(a^{2}-ab+b^{2})\)Difference of Cubes: \(a^{3}-b^{3}=(a-b)(a^{2}+ab+b^{2})\)Cube of a Sum: \((a+b)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3}\) (or \(a^{3}+b^{3}+3ab(a+b)\))Cube of a Difference: \((a-b)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3}\) (or \(a^{3}-b^{3}-3ab(a-b)\)) Quadratic Equation Standard Form: \(ax^{2}+bx+c=0\)Quadratic Formula (for roots \(x\)): \(x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}\) Laws of Exponents & Radicals \((a^{m})(a^{n})=a^{m+n}\)\((ab)^{m}=a^{m}b^{m}\)\((a^{m})^{n}=a^{mn}\)\(a^{0}=1\) (for \(a\ne 0\))