Basic Identities
SSC GD Self-Paced Course
Algebraic identities are equations that are true for all values of the variables. They are used to simplify expressions, solve equations, and perform calculations quickly.
1. Square of a Sum
Formula:
(a + b)² = a² + 2ab + b²
Example:
(x + 5)²
= x² + 2(x)(5) + 5²
= x² + 10x + 25
2. Square of a Difference
Formula:
(a - b)² = a² - 2ab + b²
Example:
(x - 3)²
= x² - 2(x)(3) + 3²
= x² - 6x + 9
3. Product of Sum and Difference
Formula:
(a + b)(a - b) = a² - b²
Example:
(x + 4)(x - 4)
= x² - 4²
= x² - 16
4. Cube of a Sum
Formula:
(a + b)³ = a³ + 3a²b + 3ab² + b³
Example:
(x + 2)³
= x³ + 3(x²)(2) + 3(x)(2²) + 2³
= x³ + 6x² + 12x + 8
5. Cube of a Difference
Formula:
(a - b)³ = a³ - 3a²b + 3ab² - b³
Example:
(x - 1)³
= x³ - 3(x²)(1) + 3(x)(1²) - 1³
= x³ - 3x² + 3x - 1
6. Sum and Difference of Cubes
Sum of Cubes:
a³ + b³ = (a + b)(a² - ab + b²)
Difference of Cubes:
a³ - b³ = (a - b)(a² + ab + b²)
7. Special Products
(x + a)² - (x - a)² = 4ax
(x + a)(x + b) = x² + (a + b)x + ab
Practice Section
Each Q followed by its Answer (SSC style). Click on "View Answer" to check your understanding.
Q1. Expand (x + 5)²
View Answer
x² + 10x + 25
Q2. Expand (x - 7)²
View Answer
x² - 14x + 49
Q3. Simplify (x + 3)(x - 3)
View Answer
x² - 9
Q4. Expand (2x + 3)²
View Answer
4x² + 12x + 9
Q5. Expand (x - 4)(x + 4)
View Answer
x² - 16
Q6. Expand (x + 2)³
View Answer
x³ + 6x² + 12x + 8
Q7. Expand (x - 1)³
View Answer
x³ - 3x² + 3x - 1
Q8. Simplify x³ + 27
View Answer
(x + 3)(x² - 3x + 9)
Q9. Simplify 8 - x³
View Answer
(2 - x)(4 + 2x + x²)
Q10. Simplify (x + 5)² - (x - 5)²
View Answer
20x
Q11. Expand (x + 3)(x + 7)
View Answer
x² + 10x + 21
Q12. Simplify (x + 2)² - (x - 2)²
View Answer
8x
Q13. Simplify (x + 1)³ + (x - 1)³
View Answer
2x³ + 6x
Q14. Expand (3x + 2)²
View Answer
9x² + 12x + 4
Q15. Simplify (x + a)(x + b)
View Answer
x² + (a + b)x + ab
✅ SSC GD Exam Strategy
🟢 Memorize all basic algebraic identities thoroughly
🟢 Practice quick expansion and simplification of expressions
🟢 Master cube identities as they frequently appear in exams
🟢 Learn to identify which identity applies to different problems
🟢 Time yourself - aim for 20-40 seconds per identity problem
You've completed Basic Algebraic Identities!
SSC GD Tip: Mastering algebraic identities is crucial for solving complex algebra problems quickly and accurately. These identities help simplify expressions, solve equations efficiently, and save valuable time in exams. Regular practice with previous year SSC GD questions will help you recognize which identity to apply in different scenarios. Pay special attention to square and cube identities as they are frequently tested. Remember that practice makes perfect - the more you work with these identities, the faster you'll become at applying them.
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