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Algebraic Identities: Formulas, Examples and Easy Ways to Remember Them
Algebraic Identities are considered one of the most valuable topics in school-level math. Algebraic identities enable students to simplify mathematical expressions, solve algebraic problems quickly, and save on unnecessary long calculations. After having knowledge about the basic formulas of algebraic identities, solving complex looking questions becomes quite easy.
Whatever the reason may be whether you are going to appear for school exams, CBSE math exams, or just want to revise your algebra basics.
What Are Algebraic Identities?
variables involved.
For example:
(a + b)² = a² + 2ab + b²
Identity since it is true for any value of a and b.
The problem arises because students often fail to distinguish between an identity and an equation. An equation may be true for some values of the variables, but not for other values.
Algebraic Identities Formula
Some of the important algebraic identities formulas are:
1. Square of a Sum
(a + b)² = a² + 2ab + b²
Example:
(5 + 2)²
= 5² + 2(5)(2) + 2²
= 25 + 20 + 4
= 49
2. Square of a Difference
(a − b)² = a² − 2ab + b²
Example:
(7 − 3)²
= 7² − 2(7)(3) + 3²
= 49 − 42 + 9
= 16
3. Difference of Two Squares
a² − b² = (a + b)(a − b)
Example:
25² − 15²
= (25 + 15)(25 − 15)
= 40 × 10
= 400
4. Product of Two Binomials
(x + a)(x + b) = x² + (a + b)x + ab
Such identities are especially helpful while working with expansions and factorization problems.
5. Cube of a Sum
(a + b)³ = a³ + 3a²b + 3ab² + b³
6. Cube of a Difference
(a − b)³ = a³ − 3a²b + 3ab² − b³
Such identities are extensively used in higher mathematics and may prove to be very time-saving in examination conditions.
How to Remember Algebraic Identities Easily
Remembering formulae without understanding them can make studying algebra difficult. Here are some simple techniques:
- Understand the pattern: So when you come across (a + b)², remind yourself “first square + twice the product + second square.”
- Practise with numbers: Put numerical values in place of variables to see if you have recalled the formulae properly.
- Write formulas regularly: Keep a small sheet of algebra formulae handy for a quick review.
- Group similar identities: Learn identities of squares first, then that of cubes, and then factorization identities.
- Solve questions: As soon as you use an identity, you will be able to remember it with practice.
Common Mistakes Students Make
A frequent mistake is writing:
(a + b)² = a² + b²
This is incorrect.
The correct formula is:
(a + b)² = a² + 2ab + b²
Students also commonly forget the middle term 2ab or make sign mistakes when working with (a − b)².
Why Are Algebraic Identities Important?
Algebraic identities help in:
- Simple expression in algebra
- Factorization of expressions
- Quick solving of mathematics problems
- Calculation of large numbers mentally
- Preparing for exam purpose
- Sound basis in algebra
Frequently Asked Questions
What are the three basic algebraic identities?
The three commonly taught identities are:
(a + b)² = a² + 2ab + b²
(a − b)² = a² − 2ab + b²
a² − b² = (a + b)(a − b)
How can I learn algebraic identities quickly?
Learn the logic behind every equation, do practice examples, and revise equations periodically rather than depending only on memorisation.
Are algebraic identities important for Class 8, 9 and 10?
Yes. Algebraic formula is an important concept that builds the base for other concepts such as factorisation, polynomial and advanced algebra. An understanding of this concept will simplify other math concepts.
Need Help With Algebra?
However, when a child knows the formulas but is unable to use them in problems, personal tutoring might help. Ziyyara’s online math tutoring lets the child get all his doubts cleared and get personalized feedback on concepts he is having trouble with.
Knowing the algebraic identities now will make learning many other mathematics topics easy for the child in the future.
Ready to make algebra easier? Start learning with Ziyyara today!
