Class 8 math formulas
Exponent rules, square and cube identities, Pythagoras, and the cube, cuboid and cylinder formulas used in Class 8 NCTB maths — the usual bridge into Class 9.
Last updated: 2026-10-06
Class 8
Lower secondary
Class 8 exponents, square and cube identities, and mensuration underpin Class 9. Apply each identity to a problem; memorising alone fails in the exam.
Exponents
Product of powers
aᵐ × aⁿ = aᵐ⁺ⁿ
Quotient of powers
aᵐ / aⁿ = aᵐ⁻ⁿ
a ≠ 0.
Power of a power
(aᵐ)ⁿ = aᵐⁿ
Power of a product
(ab)ⁿ = aⁿ bⁿ
Power of a fraction
(a/b)ⁿ = aⁿ / bⁿ
b ≠ 0.
Zero exponent
a⁰ = 1
a ≠ 0.
Negative exponent
a⁻ⁿ = 1 / aⁿ
a ≠ 0.
Algebraic identities
(a + b)²
(a + b)² = a² + 2ab + b²
(a − b)²
(a − b)² = a² − 2ab + b²
a² − b²
a² − b² = (a + b)(a − b)
(a + b)³
(a + b)³ = a³ + 3a²b + 3ab² + b³
(a − b)³
(a − b)³ = a³ − 3a²b + 3ab² − b³
a³ + b³
a³ + b³ = (a + b)(a² − ab + b²)
a³ − b³
a³ − b³ = (a − b)(a² + ab + b²)
Factorisation
Common factor
ax + ay = a(x + y)
Splitting the middle term
x² + (p + q)x + pq = (x + p)(x + q)
Square roots
Square root of a perfect square
√(a²) = |a|
Square root of a product
√(ab) = √a × √b
a ≥ 0 and b ≥ 0.
Triangles, quadrilaterals and Pythagoras
Pythagoras theorem
In a right triangle, a² + b² = c²
c is the hypotenuse, opposite the right angle.
Angle sum of a quadrilateral
∠A + ∠B + ∠C + ∠D = 360°
Area of a trapezium
A = (1/2) × (a + b) × h
a and b are the parallel sides; h is the height.
Solid mensuration
Volume of a cube
V = a³
Surface area of a cube
TSA = 6a²
Volume of a cuboid
V = l × b × h
Surface area of a cuboid
TSA = 2(lb + bh + hl)
Volume of a cylinder
V = πr²h
Curved surface of a cylinder
CSA = 2πrh
Total surface of a cylinder
TSA = 2πr(h + r)
Statistics
Mean
mean = (Σx) / n
Median (odd n)
median = middle value after arranging in order
Median (even n)
median = average of the two middle values
Mode
mode = the value that appears most often
How to use the Class 8 list
- Apply each identity to a number example — Expand (a+b)² with numbers before you factorise a messy expression.
- Name the hypotenuse in Pythagoras — c is always opposite the right angle. Mixing it with a leg is the usual error.
- SSC formulas come next — Quadratic formula and trigonometry are on Class 9–10.
Official links
- NCTB — textbooks and syllabus — The national curriculum and textbook board publishes textbooks and syllabus notices.
Source: NCTB textbook structure and syllabus
FAQ
Is there a board exam at the end of Class 8?
Not currently. These formulas still matter for the school annual exam and for Class 9. See the Class 8 suggestion for how to prepare.
Which identities must I know by heart?
(a±b)², a²−b², and the cube pair (a±b)³ / a³±b³. Class 9 still uses them inside longer algebra.