Tuesday, 2 June 2026

Bank Exam Practice Material Series Page 17 | Advanced Algebra Basics Tricks and Equation Solving Methods

Shaktimatha Learning

Ultimate Bank Exam Practice Material Series 2026

Premium Multilingual Educational Ecosystem for Bank Exams, SSC, Railways, Insurance, Government Jobs, Quantitative Aptitude, Reasoning, Mock Tests, and Speed Maths Preparation.

Algebra Basics

Equation Concepts

Heavy Standard Questions

Speed Tricks

Page 17 – Advanced Algebra Basics Tricks and Equation Solving Methods

Master advanced algebra basics, equation solving methods, algebraic identities, and shortcut solving techniques for competitive examinations.

Why Algebra is Important

Important topic in Bank and SSC exams
Strengthens logical and analytical thinking
Useful in quadratic and arithmetic problems
Improves equation-solving speed
Enhances mathematical reasoning ability

Core Concepts Covered

Linear Equations
Quadratic Equations
Algebraic Identities
Factorization Methods
Variable-Based Calculations

Important Algebra Formulas & Identities

Binomial Square Identity

Difference of Squares

Quadratic Formula

Advanced Algebra Tricks

Trick 1 – Fast Square Expansion

Find (21 + 9)²

Using identity:

21² + 2×21×9 + 9²

441 + 378 + 81

Answer = 900

Trick 2 – Difference of Squares

Find 51² − 49²

(51 − 49)(51 + 49)

2 × 100

Answer = 200

Trick 3 – Quadratic Factorization

x² − 5x + 6 = 0

Factors:

(x − 2)(x − 3)

Roots:

x = 2, 3

Heavy Standard Practice Questions

Question 1

Simplify: (15 + 5)²

Answer = 400

Question 2

Find value of 81² − 79²

Answer = 320

Question 3

Solve: x² − 7x + 12 = 0

Answer = 3, 4

Question 4

If x + y = 10 and xy = 21, find x² + y²

Answer = 58

Fast Revision Table

Concept	Shortcut Idea
Algebraic Identities	Memorize common formulas
Difference of Squares	Apply direct factorization
Quadratic Equations	Use factorization quickly
Variable Problems	Substitute logically