Maths Formula for Class 8 with Examples

Q: Which maths formula for class 8 is most important?

The algebraic identities, and especially $(a+b)^2$ and $a^2-b^2$. They appear in every later year's algebra.

Q: How do I avoid memorising every identity separately?

Learn two or three anchors and derive the rest. $(a-b)^2$ is $(a+b)^2$ with a sign flipped, and the cubic factorisations differ by one middle sign.

Key Points

The maths formula for class 8 set is dominated by the algebraic identities, which are the year's most examined formulas.
Exponent rules arrive as a compact family, and nearly all of them follow from what an exponent means.
Mensuration extends class 6 and 7 work to cylinders, cones and spheres, and to lateral as well as total surface area.
Commercial arithmetic brings profit, loss, discount and compound interest, each with its own base.
Class 8 is the year algebra becomes the main tool, so the identities carry through every later year.

What Formulas Does Class 8 Maths Cover?

The maths formula for class 8 list is substantially larger than class 7's, and its centre of gravity shifts from measurement to algebra. The identities introduced here are used constantly from this point on.

Four groups cover almost everything: algebraic identities, exponent rules, mensuration, and commercial arithmetic.

Algebraic Identities

Identity	Expansion
$(a+b)^2$	$a^2 + 2ab + b^2$
$(a-b)^2$	$a^2 - 2ab + b^2$
$a^2 - b^2$	$(a+b)(a-b)$
$(a+b)^3$	$a^3 + 3a^2b + 3ab^2 + b^3$
$a^3 + b^3$	$(a+b)(a^2-ab+b^2)$
$a^3 - b^3$	$(a-b)(a^2+ab+b^2)$
$(a+b+c)^2$	$a^2+b^2+c^2+2ab+2bc+2ca$

The a plus b whole square and difference of squares formula pages cover the two most used in detail, and a cube plus b cube handles the cubic pair.

Exponent Rules

Rule	Formula
Product	$a^m \times a^n = a^{m+n}$
Quotient	$\frac{a^m}{a^n} = a^{m-n}$
Power of a power	$(a^m)^n = a^{mn}$
Zero exponent	$a^0 = 1$ , $a \neq 0$
Negative exponent	$a^{-n} = \frac{1}{a^n}$
Product to a power	$(ab)^m = a^m b^m$

Every rule here follows from exponents counting repeated multiplication, which is why they are worth deriving once rather than memorising six times.

Mensuration

Solid or shape	Formula
Cylinder volume	$\pi r^2 h$
Cylinder curved surface	$2\pi r h$
Cone volume	$\frac{1}{3}\pi r^2 h$
Cone curved surface	$\pi r l$
Sphere volume	$\frac{4}{3}\pi r^3$
Sphere surface area	$4\pi r^2$
Trapezium area	$\frac{1}{2}(a+b)h$
Rhombus area	$\frac{1}{2}d_1 d_2$

The cone's curved surface needs the slant height formula rather than the vertical height, which is the most common slip in this group.

Commercial Arithmetic

Quantity	Formula	Base
Profit percentage	$\frac{\text{SP}-\text{CP}}{\text{CP}} \times 100$	cost price
Loss percentage	$\frac{\text{CP}-\text{SP}}{\text{CP}} \times 100$	cost price
Discount percentage	$\frac{\text{MP}-\text{SP}}{\text{MP}} \times 100$	marked price
Simple interest	$\frac{PRT}{100}$	principal
Compound amount	$P\left(1+\frac{R}{100}\right)^n$	principal

Each percentage here sits on a different base, which is the single most important thing to keep straight. The discount formula and interest formula pages set those bases out.

Examples of Maths Formula for Class 8

Example 1

Expand $(x+5)^2$ .

$x^2 + 2(x)(5) + 25 = x^2 + 10x + 25$

Final answer: $x^2 + 10x + 25$

Example 2

Expand $(x+5)^2$ as $x^2 + 25$ .

Squaring looks like it should apply to each term, giving $x^2 + 25$ .

Testing with $x = 1$ settles it: $(1+5)^2 = 36$ , while $1 + 25 = 26$ . The two differ by 10, which is exactly the $2ab$ term that was dropped.

$(x+5)^2 = x^2 + 10x + 25$

Final answer: $x^2 + 10x + 25$ . Substituting a small number is the fastest check on any expansion.

Example 3

Simplify $\frac{2^7 \times 2^3}{2^8}$ .

Use the product rule then the quotient rule:

$\frac{2^{10}}{2^8} = 2^{2} = 4$

Final answer: 4

Example 4

Find the volume of a cone of radius 3 cm and height 7 cm, taking $\pi = \frac{22}{7}$ .

$V = \frac{1}{3} \times \frac{22}{7} \times 9 \times 7 = 66$

Final answer: 66 cm³

Example 5

An item bought for 400 is sold for 460. Find the profit percentage.

$\frac{460-400}{400} \times 100 = \frac{60}{400} \times 100 = 15$

Final answer: 15 per cent

How the Class 8 Formulas Connect

The identities are not seven separate facts. $(a-b)^2$ is $(a+b)^2$ with a sign changed, and the two cubic factorisations differ only in one middle sign, so the family can be rebuilt from two or three anchors.

Mensuration follows the same economy. A cone's volume is a third of the cylinder's with the same base and height, and a sphere's surface area is exactly four times the area of its great circle.

Seeing those relationships cuts the memorising roughly in half, which matters because class 9 and class 10 assume all of it.

Where Class 8 Students Trip Up

Mistake 1: Distributing a square over a sum

Where it slips in: The square sits outside a bracket, and squaring each term inside looks like expanding.

Don't do this: $(a+b)^2 = a^2 + b^2$

The correct way: $(a+b)^2 = a^2+2ab+b^2$ . The middle term is the whole point of the identity.

Students who substitute a small number such as $a=1$ , $b=2$ into both sides catch this in seconds. A numerical test on an identity is quicker than re-deriving it and works on every expansion in the list.

Mistake 2: Using vertical height for a cone's curved surface

Where it slips in: The question gives the height, and the formula asks for a length.

Don't do this: $\pi r h$ for curved surface area.

The correct way: $\pi r l$ , with $l$ the slant height found from $\sqrt{r^2+h^2}$ . Volume uses the vertical height; curved surface uses the slant.

Mistake 3: Mixing up the percentage bases

Where it slips in: Profit, loss and discount all produce a percentage from two prices.

Don't do this: Divide a discount by the cost price.

The correct way: Profit and loss sit on the cost price; discount sits on the marked price. Identifying the base before dividing is most of the work.

The Short Version

The maths formula for class 8 set covers algebraic identities, exponent rules, mensuration and commercial arithmetic.
The identities are the year's most examined formulas, and the middle term is where most marks are lost.
Cone and sphere mensuration relates back to the cylinder and the circle, which reduces what must be learned.
Every commercial percentage has its own base, so identifying the base comes before the arithmetic.
To work through the class 8 syllabus with a teacher, explore an 8th grade math tutor or math classes online.

Practice These Three Before Moving On

Expand $(2x-3)^2$ and factorise $49y^2-16$ . Then find the curved surface area of a cone with radius 5 cm and height 12 cm.

Want a live Bhanzu trainer to walk through the class 8 formulas? Book a free demo class.

Was this article helpful?

Your feedback helps us write better content

Frequently Asked Questions

What is the full maths formula for class 8 list?

The algebraic identities, the six exponent rules, mensuration for cylinders, cones, spheres, trapeziums and rhombuses, and commercial arithmetic for profit, loss, discount and interest.

Which maths formula for class 8 is most important?

The algebraic identities, and especially

(a+b)^2

and

a^2-b^2

. They appear in every later year's algebra.

How do I avoid memorising every identity separately?

Learn two or three anchors and derive the rest.

(a-b)^2

(a+b)^2

with a sign flipped, and the cubic factorisations differ by one middle sign.

What changes between class 7 and class 8 formulas?

Class 8 shifts the emphasis from measurement to algebra, introducing the identities and exponent rules that later years assume.

✍️ Written By

Bhanzu Team

Content Creator and Editor

Bhanzu’s editorial team, known as Team Bhanzu, is made up of experienced educators, curriculum experts, content strategists, and fact-checkers dedicated to making math simple and engaging for learners worldwide. Every article and resource is carefully researched, thoughtfully structured, and rigorously reviewed to ensure accuracy, clarity, and real-world relevance. We understand that building strong math foundations can raise questions for students and parents alike. That’s why Team Bhanzu focuses on delivering practical insights, concept-driven explanations, and trustworthy guidance-empowering learners to develop confidence, speed, and a lifelong love for mathematics.

Probability A Intersection B Formula with Examples

Expected Value Formula with Worked Examples

Conditional Probability Formula with Examples

Empirical Probability Formula with Examples