Algebra Notes for Class 11/12 & Competitive Exams – Handwritten Style, Study notes of Mathematics

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Algebra Notes

For Class 11/12 and Competitive Exams

Uploaded on Docsity | 15 April 2025

1. Important Algebraic Identities

(1) (a + b)^2 = a^2 + 2ab + b^ (2) (a - b)^2 = a^2 - 2ab + b^ (3) (a + b)(a - b) = a^2 - b^ (4) (x + a)(x + b) = x^2 + (a + b)x + ab (5) (x + y + z)^2 = x^2 + y^2 + z^2 + 2xy + 2yz + 2zx Tip: Memorize these as they help in quick simplifications.

2. Factorisation Techniques

Factor common terms, use identities, and apply splitting the middle term.

Example: x^2 + 7x + 10 = (x + 5)(x + 2) Use the method of middle-term splitting: 7 = 5 + 2, 5*2 = 10

3. Quadratic Equations

Standard form: ax^2 + bx + c = 0

Quadratic Formula: x = [-b ± sqrt()(b^2 - 4ac)] / 2a

Discriminant (D = b^2 - 4ac):

• D > 0: Two real and distinct roots
• D = 0: Two real and equal roots