IMPORTANT ALGEBRA FORMULAS

 

Important Algebra Formulas

1. Basic Algebraic Identities

1. (a + b)² = a² + 2ab + b²
2. (a - b)² = a² - 2ab + b²
3. a² - b² = (a + b)(a - b)
4. (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
5. (a - b - c)² = a² + b² + c² - 2(ab + bc + ca)

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2. Cube Identities

1. (a + b)³ = a³ + b³ + 3ab(a + b)
2. (a - b)³ = a³ - b³ - 3ab(a - b)
3. a³ + b³ = (a + b)(a² - ab + b²)
4. a³ - b³ = (a - b)(a² + ab + b²)

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3. Factorization Formulas

1. x² + (a + b)x + ab = (x + a)(x + b)
2. x³ + y³ + z³ - 3xyz = (x + y + z)(x² + y² + z² - xy - yz - zx)

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4. Quadratic Equation Formula

For an equation ax² + bx + c = 0, the roots are:

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

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5. Arithmetic and Geometric Progression (AP & GP)

• Sum of n terms of an AP:

  S_n = \frac{n}{2} (2a + (n-1)d)

  a_n = a + (n-1)d

  S_n = \frac{a(1 - r^n)}{1 - r}, \quad \text{if } r \neq 1

  a_n = a r^{n-1}

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6. Binomial Theorem (For Positive Integer n)

(a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k

These formulas are essential for solving algebraic problems efficiently.