Algebraic Identities Chart — Full Chart & Quick Revision
Complete reference of essential algebraic identities and formulas. Vital for simplifying expressions, factoring, and solving algebraic equations quickly.
TL;DR: Complete reference of essential algebraic identities and formulas. Vital for simplifying expressions, factoring, and solving algebraic equations quick…
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
Complete reference of essential algebraic identities and formulas. Vital for simplifying expressions, factoring, and solving algebraic equations quickly.
Algebraic Identities Chart — Full Chart
| Item | Value |
|---|---|
| (a + b)^2 | a^2 + 2ab + b^2 |
| (a - b)^2 | a^2 - 2ab + b^2 |
| (a + b)(a - b) | a^2 - b^2 |
| (a + b)^3 | a^3 + 3a^2b + 3ab^2 + b^3 |
| (a - b)^3 | a^3 - 3a^2b + 3ab^2 - b^3 |
| a^3 + b^3 | (a + b)(a^2 - ab + b^2) |
| a^3 - b^3 | (a - b)(a^2 + ab + b^2) |
| (a + b + c)^2 | a^2 + b^2 + c^2 + 2ab + 2bc + 2ca |
| a^2 + b^2 | (a + b)^2 - 2ab |
| (x + a)(x + b) | x^2 + (a + b)x + ab |
| a^4 - b^4 | (a^2 + b^2)(a^2 - b^2) |
| a^4 + a^2b^2 + b^4 | (a^2 + ab + b^2)(a^2 - ab + b^2) |
| (a + b)^2 - (a - b)^2 | 4ab |
| (a + b)^2 + (a - b)^2 | 2(a^2 + b^2) |
| (a + b + c)^3 | a^3 + b^3 + c^3 + 3(a + b)(b + c)(c + a) |
| a^3 + b^3 + c^3 - 3abc | (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca) |
| (a - b - c)^2 | a^2 + b^2 + c^2 - 2ab + 2bc - 2ca |
| a^n - b^n | (a - b)(a^(n-1) + a^(n-2)b + ... + ab^(n-2) + b^(n-1)) |
| (x + y)^2 = x^2 + y^2 if | xy = 0 |
| x^2 - (a + b)x + ab | (x - a)(x - b) |
FAQs
How do I expand (a + b + c)^2?
Using the identity: (a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca. You can also expand step by step: (a + b + c)^2 = [(a + b) + c]^2.
What is the fastest way to factor a^3 - b^3?
Use the identity: a^3 - b^3 = (a - b)(a^2 + ab + b^2). This is much faster than polynomial long division.