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Last Modified 10-03-2024

Algebra Formulas for Class 10: Complete List, Solved Examples

Algebra Formulas for Class 10: Algebra is a branch of mathematics that helps solve mathematical equations and calculate unknown numbers like variable values, constants, and percentages. When both fixed and dynamic components are present at the same time, algebra is utilised to identify a condition. The different branches of algebra are Elementary Algebra, Advanced Algebra, Abstract Algebra, Linear Algebra, and Commutative Algebra.

In this article, we have provided algebra math formulas which are required for students to achieve academic success. Students also learn how to calculate distance, profit, and loss, as well as height and container volume. It is necessary for students. It is essential for students to learn the algebra maths formulas in their academics. continue reading the article to know all about algebra formulas for class 10, vector algebra formulas, and linear algebra formulas.

List of Algebra Math Formulas for Class 10

Students who are looking for the formula of Algebra Class 10 can refer to this article. We have also provided a one-click downloadable PDF below these formulas.

Algebraic Identities for Class 10
1. (a + b)² = a²+ 2ab + b²
2. (a − b)² = a²− 2ab + b²
3. (a + b)(a – b) = a²– b²
4. (x + a)(x + b) = x²+ (a + b)x + ab
5. (x + a)(x – b) = x²+ (a – b)x – ab
6. (x – a)(x + b) = x² + (b – a)x – ab
7. (x – a)(x – b) = x²– (a + b)x + ab
8. (a + b)³ = a³+ b³+ 3ab(a + b)
9. (a – b)³ = a³– b³– 3ab(a – b)
10. (x + y + z)² = x²+ y²+ z²+ 2xy + 2yz + 2xz
11. (x + y – z)² = x²+ y²+ z²+ 2xy – 2yz – 2xz
12. (x – y + z)² = x²+ y²+ z²– 2xy – 2yz + 2xz
13. (x – y – z)² = x²+ y²+ z²– 2xy + 2yz – 2xz
14. x³+ y³+ z³– 3xyz = (x + y + z)(x²+ y²+ z²– xy – yz − xz)
15. x²+ y² =12[(x + y)²+ (x – y)²]

16. (x + a)(x + b)(x + c) = x³+ (a + b + c)x²+ (ab + bc + ca)x + abc
17. x³+ y³ = (x + y)(x²– xy + y²)
18. x³– y³ =(x – y)(x²+ xy + y²)
19. x²+ y²+ z²− xy – yz – zx = 1/2[(x − y)²+ (y − z)²+ (z − x)²]

Quadratic Formula
For ax² + bx + c = 0,
(α, β) = [–b ± √(b² – 4ac)]/2ac, where α and β are the roots of the equation.
(i) If b² − 4ac > 0, then the quadratic equation has two distinct real roots.
(ii) If b² − 4ac < 0, then the quadratic equation has two imaginary roots.
(iii) If b² − 4ac = 0, then the quadratic equation has two equal real roots.

Progression Formulas
(i) n^th term of an arithmetic sequence: a_n = a + (n – 1)d
(ii) Sum of n terms of an arithmetic sequence: S_n = n/2 [2a + (n – 1)d]
(iii) n^th term of a geometric sequence: a_n = a.r^n-1
(iv) Sum of n terms of a geometric sequence: S_n = a(1 – rⁿ)/(1 – r), r≠1
(v) Sum of infinite terms of a geometric sequence: S = a/(1 – r)

Linear Equation in Two Variables
The pair of linear equations in two variables is given as:
a₁x+b₁+c₁=0 and a₂x+b₂+c₂=0
Where a₁, b₁, c₁, & a₂, b₂, c₂ are real numbers & a₁²+b₁² ≠ 0 & a₂²+ b₂² ≠ 0
This equation has infinite possible solutions.

Check out other important Maths articles for Class 10:

NCERT Solutions for Class 10 Maths	Class 10 Maths Syllabus
NCERT Books for Class 10 Maths	Maths Formulas for Class 10 PDF Download

We have provided the direct link to download Algebra Formulas Class 10 PDF SSC. Algebra formulas for class 10 with examples will not only help Class 10 students but SSC aspirants as well in their preparation.

Importance of Algebra Formulas for Class 10

With each Class, the difficulty level of mathematical problems gradually increases, necessitating an efficient and quick computation technique. To answer complicated problems quickly, one must be highly familiar with the application of Algebra formulas for Class 10. Whether it’s problems involving linear equations or factorization, a thorough understanding of algebraic expressions allows the student to offer an accurate solution quickly. We at Embibe have compiled a collection of all Algebra Class 10 formulas that will not only assist you in passing your school and board examinations but will also give you confidence as you prepare for competitive exams.

Class 10 Algebra Math Formulas Questions

We have provided some important Class 10 Algebra questions with solutions:

Question 1: Find the roots of the equation x² – 3x – m (m + 3) = 0, where m is a constant.

Solution: x² – 3x – m(m + 3) = 0 (Given)
Comparing it with the general form: ax² + bx + c = 0, we get:
a = 1, b = -3, and c = – m (m + 3)
We know that, D = (b² – 4ac)
So
D = (- 3)² – 4(1) [-m(m + 3)]
= 9 + 4m (m + 3)
= 4m² + 12m + 9
= (2m + 3)²
Putting the value of D in the quadratic formula: (α, β) = [–b ± √D]/2ac, we get:
(α, β) = [–3 ± √(2m + 3)²]/2x1x- m (m + 3)
Solving this equation, we get
(α, β) = (m + 3, -m)
So, the roots of the given quadratic equation are (m + 3) and -m.

Question 2: If 1 is a root of the equations ay² + ay + 3 = 0 and y² + y + b = 0, then find the value of ab.

Solution: ay² + ay + 3 = 0 (Given).
Putting the value of y = 1 in the equation, we get:
a(1)² + a(1) + 3 = 0
2a = -3
a = −3/2
Similarly, y² + y + b = 0 (Given).
Putting the value of y = 1 in the equation, we get
1² + 1 + b = 0
b = -2
∴ ab = (−3/2)(−2) = 3

Question 3: If the quadratic equation px\frac{1}{2} – 25–√ px + 15 = 0 has two equal roots, then find the value of p.

Solution: The given quadratic equation can be written as px\frac{1}{2} – 25–√ px + 15 = 0
Here a = p, b = – 25–√ p, c = 15
For equal roots, D = 0
D = b² – 4ac – 0 …[∵ Equal roots]
0 = (-25–√p)² – 4 × p × 15
0 = 4 × 5p² – 60p
0 = 20p² – 60p => 20p² = 60p
p = 60p20p = 3
∴ p = 3
Hence, the value of p is 3.

Question 4: Find the value of p so that the quadratic equation px(x – 3) + 9 = 0 has two equal roots.

Solution: We have, px (x – 3) + 9 = 0 (Given)
px² – 3px + 9 = 0 Here a = p, b = -3p,
∵ D = 0 (Given)
b² – 4ac = 0
⇒ (-3p)² – 4(p)(9) = 0
⇒ 9p² – 36p = 0
⇒ 9p (p – 4) = 0
⇒ 9p = 0 or p – 4= 0
p = 0 (rejected) or p = 4
∴ p = 4 (∵ Coeff. of x² cannot be zero)
Hence, the value of p is 4.

Question 5: Find the value of m so that the quadratic equation mx (x – 7) + 49 = 0 has two equal roots.

Solution: We have, mx (x – 7) + 49 = 0
mx² – 7mx + 49 = 0 (Given)
Here, a = m, b = – 7m, c = 49
D = b² – 4ac = 0 [For equal roots]
⇒ (-7m)² – 4(m) (49) = 0
⇒ 49m² – 4m (49) = 0
⇒ 49m (m – 4) = 0
⇒ 49m = 0 or m – 4 = 0
m = 0 (rejected) or m = 4
∴ m = 4
Hence, the value of m is 4.

Check Algebra Formulas for other classes as well:

Algebra Formulas for Class 8

Algebra Formulas for Class 9

Practice Questions on Maths Formulas for Class 10 Algebra

Here we have provided some of the practice questions on the formula of algebraic expression for Class 10 for you to practice:

Q1: Simplify the algebraic expression -2(x – 3) + 4(-2 x + 8)

Q2: Expand and simplify the algebraic expression (x + 3)(x – 3) – (-x – 9)

Q3: For what value of k is the point (-2, k) on the line with equation -3 x + 3 y = 4?

Q4: For what value of a will the system given below have no solutions?
(i) 2x + 6y = -2
(ii) -3x + ay = 4

Q5: Which line given by its equation below contains the points (1, -1) and (3, 5)?
a) -2y -6x = 0
b) 2y = 6x – 8
c) y = 3x + 4
d) y = -3x + 4

Q6: Solve for x the equation (1/2)x² + mx – 2 = 0

Q7: For what values of k the equation -x² + 2kx – 4 = 0 has one real solution?

Q8: For what values of b the equation x² – 4x + 4b = 0 has two real solutions?

Q9: Simplify: |- x| + |3 x| – |- 2 x| + 3|x|

Q10: If (x² – y²) = 10 and (x + y) = 2, find x and y.

Q11: Had Ram scored 10 more marks in her mathematics test out of 30 marks, 9 times these marks would have been the square of her actual marks. How many marks did she get in the test?

Q12: Find a natural number whose square diminished by 84 is thrice of 8 more of given number.

Q13: If- 5 is a root of the quadratic equation 2x² + px – 15 = 0 and the quadratic equation p(x² + x) + k = 0 has equal roots, find the value of k.

Q14: What is the value of x: √3x² – 2√2x – 2√3 = 0?

Q15: The roots of the equation x² − 3x − 10 = 0 are:
(i) real and equal
(ii) real and unequal
(iii) imaginary and unequal
(iv) real and imaginary

Also, Check

Trigonometry Formulas	Algebra Formulas
Mensuration Formulas	Differentiation Formulas

FAQs on Algebra Formulas for Class 10

Q1: What are the basics of algebra?
Ans: The basics of algebra are:
(i) Addition and subtraction of algebraic expressions
(ii) Multiplications and division of algebraic expression
(iii) Solving equations
(iv) Literal equations and formulas
(v) Applied verbal problems

Q2: What are the different types of algebraic equations?
Ans: The different types of algebraic equations are:
(i) Monomial or polynomial equations
(ii) Exponential equations
(iii) Trigonometric equations
(iv) Logarithmic equations
(v) Rational equations

Q3: What is Algebra and why do we need it?
Ans: Algebra teaches you to follow a logical path to solve a problem. This, in turn, allows you to have a better understanding of how numbers function and work together in an equation. By having a better understanding of numbers, you’ll be better able to do any type of math.

Q4: What is an algebraic equation?
Ans: An algebraic equation or identity is made of two or more algebraic expressions separated by an equal sign. The LHS (Left Hand Side) of the equation is always equal to the RHS (Right Hand Side) for any value of variables in it.ns

Q5: What are the chapters in Algebra Class 10?
Ans: The following chapters for Class 10 maths contain Algebra concepts:
(i) Arithmetic Progressions
(ii) Quadratic Equations
(iii) Pair of Linear Equations in Two Variables
(iv) Polynomials
(v) Real Numbers