CBSE · Class 8–10

Algebra Formulas — Class 8, 9 and 10

Q: What are the most important algebraic identities for Class 10 boards?

The five most exam-important algebraic identities for Class 10 CBSE are: (1) (a+b)² = a²+2ab+b², (2) (a−b)² = a²−2ab+b², (3) (a+b)(a−b) = a²−b², (4) (a+b)³ and (a−b)³ expansions, and (5) a³+b³ and a³−b³ factorisation formulas. These appear in 2–5 mark questions across algebra chapters. Know them forwards and backwards — both for expanding and for factorising.

Q: How do I remember the quadratic formula?

The quadratic formula x = (−b ± √(b²−4ac)) / 2a can be memorised as: 'negative b, plus or minus root of b-squared minus 4ac, all over 2a.' Alternatively, derive it yourself by completing the square on ax²+bx+c=0 — once you understand the derivation, you will never forget it. The discriminant b²−4ac tells you: positive = 2 roots, zero = 1 root (repeated), negative = no real roots.

Q: What is the difference between an identity and an equation?

An algebraic identity is true for ALL values of the variable (e.g., (a+b)² = a²+2ab+b² is true for every value of a and b). An equation is true only for specific values of the variable (e.g., x²−5x+6=0 is only true for x=2 and x=3). This distinction matters in exams: 'verify the identity' means show it is true for all values; 'solve the equation' means find the specific value(s).

All essential algebra formulas for CBSE Class 8–10 — algebraic identities, factorisation, laws of exponents, quadratic equations and polynomial theorems.

5 chapters33+ formulasCBSE 2026–27

Ch 1 Ch 2 Ch 3 Ch 4 Ch 5

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For reference only. Always verify formulas and information against your official NCERT textbooks or board-prescribed materials before use in exams. Learnizo does not guarantee absolute accuracy.

Ch 1.Basic Algebraic Identities

Formula / Relation	Expression	Note
(a + b)²	(a + b)² = a² + 2ab + b²	Expand or recognise square of a binomial
(a − b)²	(a − b)² = a² − 2ab + b²	Note: (a − b)² ≥ 0, so a² + b² ≥ 2ab
(a + b)(a − b)	(a + b)(a − b) = a² − b²	Difference of squares — very commonly used in factorisation
(x + a)(x + b)	(x + a)(x + b) = x² + (a + b)x + ab	Used to factorize quadratics of the form x² + bx + c
(a + b + c)²	(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca	Class 9 identity — often tested in 2–3 mark questions
(a + b)³	(a + b)³ = a³ + 3a²b + 3ab² + b³ = a³ + b³ + 3ab(a + b)	Class 9 — cube of a binomial
(a − b)³	(a − b)³ = a³ − 3a²b + 3ab² − b³ = a³ − b³ − 3ab(a − b)
a³ + b³	a³ + b³ = (a + b)(a² − ab + b²)	Sum of cubes factorisation
a³ − b³	a³ − b³ = (a − b)(a² + ab + b²)	Difference of cubes factorisation
a³ + b³ + c³ − 3abc	a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − ab − bc − ca)	If a + b + c = 0, then a³ + b³ + c³ = 3abc

Ch 2.Laws of Exponents

Formula / Relation	Expression	Note
Product rule	aᵐ × aⁿ = aᵐ⁺ⁿ	Multiply → add exponents (same base)
Quotient rule	aᵐ ÷ aⁿ = aᵐ⁻ⁿ	Divide → subtract exponents (same base)
Power of a power	(aᵐ)ⁿ = aᵐⁿ	Power of a power → multiply exponents
Power of a product	(ab)ⁿ = aⁿbⁿ
Power of a quotient	(a/b)ⁿ = aⁿ/bⁿ
Zero exponent	a⁰ = 1 (a ≠ 0)	Any non-zero number to the power 0 is 1
Negative exponent	a⁻ⁿ = 1/aⁿ	Negative exponent = reciprocal
Fractional exponent	a^(1/n) = ⁿ√a	Fractional exponent = nth root

Ch 3.Polynomial Theorems (Class 9)

Formula / Relation	Expression	Note
Remainder Theorem	When p(x) is divided by (x − a), remainder = p(a)	To find remainder: substitute x = a into p(x)
Factor Theorem	(x − a) is a factor of p(x) ⟺ p(a) = 0	If remainder is 0, the divisor is a factor; converse also true
Linear polynomial	p(x) = ax + b has one zero: x = −b/a	One zero = one root
Quadratic zeros (sum & product)	For ax² + bx + c: sum of zeros = −b/a, product of zeros = c/a	Also known as Vieta's formulas; used to form a quadratic from given roots
Cubic zeros	For ax³ + bx² + cx + d: Σα = −b/a, Σαβ = c/a, αβγ = −d/a	Sum of roots, sum of products of pairs, product of all three roots

Ch 4.Quadratic Equations (Class 10)

Formula / Relation	Expression	Note
Standard form	ax² + bx + c = 0, where a ≠ 0	Must be in this form before applying quadratic formula
Quadratic Formula	x = (−b ± √(b² − 4ac)) / 2a	Works for all quadratic equations; ± gives two roots
Discriminant (D)	D = b² − 4ac	D > 0: two distinct real roots; D = 0: two equal real roots; D < 0: no real roots
Sum of roots	α + β = −b/a	Without solving the equation
Product of roots	α × β = c/a
Form quadratic from roots	x² − (α + β)x + αβ = 0	If you know the sum and product of roots, you can write the equation directly

Ch 5.Arithmetic Progressions (Class 10)

Formula / Relation	Expression	Note
nth term (Tₙ)	Tₙ = a + (n − 1)d	a = first term, d = common difference, n = term number
Sum of n terms (Sₙ)	Sₙ = n/2 × [2a + (n − 1)d]	Also written as Sₙ = n/2 × (first term + last term)
Common difference (d)	d = Tₙ − Tₙ₋₁ (any consecutive pair)	Constant difference between consecutive terms
Sum when last term known	Sₙ = n/2 × (a + l)	l = last term (Tₙ)

Frequently Asked Questions

What are the most important algebraic identities for Class 10 boards?

The five most exam-important algebraic identities for Class 10 CBSE are: (1) (a+b)² = a²+2ab+b², (2) (a−b)² = a²−2ab+b², (3) (a+b)(a−b) = a²−b², (4) (a+b)³ and (a−b)³ expansions, and (5) a³+b³ and a³−b³ factorisation formulas. These appear in 2–5 mark questions across algebra chapters. Know them forwards and backwards — both for expanding and for factorising.

How do I remember the quadratic formula?

The quadratic formula x = (−b ± √(b²−4ac)) / 2a can be memorised as: 'negative b, plus or minus root of b-squared minus 4ac, all over 2a.' Alternatively, derive it yourself by completing the square on ax²+bx+c=0 — once you understand the derivation, you will never forget it. The discriminant b²−4ac tells you: positive = 2 roots, zero = 1 root (repeated), negative = no real roots.

What is the difference between an identity and an equation?

An algebraic identity is true for ALL values of the variable (e.g., (a+b)² = a²+2ab+b² is true for every value of a and b). An equation is true only for specific values of the variable (e.g., x²−5x+6=0 is only true for x=2 and x=3). This distinction matters in exams: 'verify the identity' means show it is true for all values; 'solve the equation' means find the specific value(s).

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