Class 8 — Maths Formula Sheet

(a + b)² = a² + 2ab + b²

Square of sum of two terms.

💡 (3+4)² = 9+24+16 = 49

(a − b)² = a² − 2ab + b²

Square of difference of two terms.

💡 (5−2)² = 25−20+4 = 9

a² − b² = (a + b)(a − b)

Difference of squares factorisation.

💡 9² − 4² = (9+4)(9−4) = 65

(a + b)³ = a³ + 3a²b + 3ab² + b³

Cube of sum.

💡 (1+2)³ = 1+6+12+8 = 27

(a − b)³ = a³ − 3a²b + 3ab² − b³

Cube of difference.

a³ + b³ = (a + b)(a² − ab + b²)

Sum of cubes factorisation.

a³ − b³ = (a − b)(a² + ab + b²)

Difference of cubes factorisation.

aᵐ × aⁿ = aᵐ⁺ⁿ

Multiply powers with the same base: add exponents.

aᵐ ÷ aⁿ = aᵐ⁻ⁿ

Divide powers with the same base: subtract exponents.

(aᵐ)ⁿ = aᵐⁿ

Raise a power to another power: multiply exponents.

a⁰ = 1  (a ≠ 0)

Any non-zero base raised to 0 equals 1.

a⁻ⁿ = 1 / aⁿ

Negative exponent means reciprocal.

A = ½ × (a + b) × h

Half the sum of parallel sides times height.

📌 a, b = parallel sides, h = height

A = ½ × d₁ × d₂

Half product of diagonals.

📌 d₁, d₂ = diagonals

V = a³

Side cubed.

📌 a = side length

V = l × b × h

Length × breadth × height.

📌 l = length, b = breadth, h = height

V = πr²h

Base area times height.

📌 r = radius, h = height

CSA = 2πrh

Curved surface area of cylinder.

📌 r = radius, h = height

TSA = 2πr(r + h)

Total surface area including both circular ends.

y/x = k  (constant)
y = kx

As x increases, y increases in the same ratio.

xy = k  (constant)
y = k/x

As x increases, y decreases proportionally.