Algebra Formulas
Algebra Formulas – 60-Second Revision Sheet
Must-Know Identities
(a+b)² = a² + 2ab + b²(a−b)² = a² − 2ab + b²a² − b² = (a−b)(a+b)(difference of squares = “minus-plus trick”)(a+b)³ = a³ + b³ + 3ab(a+b)(a−b)³ = a³ − b³ − 3ab(a−b)a³ + b³ = (a+b)(a² − ab + b²)a³ − b³ = (a−b)(a² + ab + b²)(x+a)(x+b) = x² + (a+b)x + ab
Linear Equation Pair
ax + by = c&dx + ey = f
Cross-method:x = (ce-bf)/(ae-bd),y = (af-cd)/(ae-bd)(write → ✕ cancel)
Quadratic Equation ax² + bx + c = 0
- Roots:
x = [−b ± √(b² − 4ac)] / 2a - Discriminant
D = b² − 4acD > 0→ real & distinctD = 0→ real & equalD < 0→ complex
Indices (Powers) – 5-Law Kit
| Law | Trick | Example |
|---|---|---|
aᵐ · aⁿ = aᵐ⁺ⁿ |
“plus while multiplying” | 2³·2⁵ = 2⁸ |
aᵐ / aⁿ = aᵐ⁻ⁿ |
“minus while dividing” | 5⁷/5² = 5⁵ |
(aᵐ)ⁿ = aᵐⁿ |
“power-on-power → multiply” | (3²)⁴ = 3⁸ |
a⁰ = 1 (a≠0) |
“zero power = hero 1” | π⁰ = 1 |
a⁻ᵐ = 1/aᵐ |
“minus flips down” | 4⁻² = 1/16 |
Surds – Two Golden Rules
√a · √b = √(ab)√a / √b = √(a/b)- Rationalise
1/(√a + √b)→ multiply by(√a − √b)/(√a − √b)(flip sign)
Series Quickies
1 + 2 + … + n = n(n+1)/21² + 2² + … + n² = n(n+1)(2n+1)/61³ + 2³ + … + n³ = [n(n+1)/2]²(sum cubes = square of sum)
Rapid-Fire MCQs
49² − 1equals
A) 50 × 48 B) 48² C) 2400 D) 2500- If
x² − 5x + 6 = 0, roots are
A) 2,3 B) −2,−3 C) 1,6 D) −1,−6 √12 × √3is
A) 6 B) 36 C) 4√3 D) 9(a−b)² + 4abequals
A)a² + b²B)(a+b)²C)a² − b²D)2ab2⁵ · 2⁻³equals
A) 4 B) 2 C) 1/4 D) 32- Sum
1 + 2 + … + 20equals
A) 190 B) 210 C) 200 D) 220 - Rationalising factor of
1/(√7 − √5)is
A)√7 − √5B)√7 + √5C)√5D)1/√7 - If
x + 1/x = 5,x² + 1/x²is
A) 23 B) 25 C) 27 D) 24 - Discriminant of
3x² − 2x + 5 = 0is
A) −56 B) 64 C) 46 D) 0 a³ − b³whena = 4, b = 2equals
A) 56 B) 64 C) 8 D) 48
BETA
