Algebra Formulas Notes for SSC Exams

Algebra gives three to five questions in SSC Tier 1 and many more in Tier 2. Most of them can be solved in seconds if you know a few identities and tricks. These algebra formulas notes for SSC give you all the important identities in one place, with the x plus 1/x tricks, solved examples and practice questions.

Important Algebra Identities

The x Plus 1/x Tricks

Special Rules

• If a + b + c = 0, then a cubed + b cubed + c cubed = 3abc.
• If a + b = s and ab = p, then a squared + b squared = s squared - 2p and a cubed + b cubed = s cubed - 3ps.
• If a - b = d and ab = p, then a squared + b squared = d squared + 2p.
• To find a squared - b squared quickly for numbers like 101 and 99, use (a + b)(a - b).

Linear Equations

A linear equation in one variable can be solved by taking the variable terms to one side and the constants to the other side. For two equations, use elimination: multiply the equations to make the coefficients of one variable equal, then add or subtract them. For ax + by = c and dx + ey = f, a unique solution exists when ae is not equal to bd.

Solved Examples

Example 1: If a + b = 7 and ab = 12, find a squared + b squared.
Solution: a squared + b squared = (a + b) squared - 2ab = 49 - 24 = 25.

Example 2: If x + 1/x = 5, find x squared + 1/x squared.
Solution: Value = k squared - 2 = 25 - 2 = 23.

Example 3: Find the value of 101 squared - 99 squared.
Solution: (101 + 99)(101 - 99) = 200 x 2 = 400.

Example 4: If a - b = 3 and ab = 10, find a squared + b squared.
Solution: Value = (a - b) squared + 2ab = 9 + 20 = 29.

Example 5: If x + 1/x = 3, find x cubed + 1/x cubed.
Solution: Value = k cubed - 3k = 27 - 9 = 18.

Example 6: If a + b + c = 0, find (a cubed + b cubed + c cubed) / abc.
Solution: Since a + b + c = 0, a cubed + b cubed + c cubed = 3abc. So the value is 3.

Quick Tips to Solve Faster

• Learn the identities in both directions (expand and factorise).
• For x + 1/x problems, use the formula directly instead of finding x.
• Check whether a + b + c = 0 first in any cube-sum question.
• Use (a + b)(a - b) to find the difference of squares of large numbers.
• Substitute a simple value like 1 or 0 to check an identity.

Common Mistakes to Avoid

• Writing (a + b) squared as a squared + b squared.
• Mixing up the signs in the cube formulas.
• Using the wrong formula for x - 1/x.
• Ignoring the special condition a + b + c = 0.
• Taking square roots without considering both signs where needed.

Quick Revision Points

• a squared + b squared = (a + b) squared - 2ab.
• x + 1/x = k: square sum = k squared - 2 and cube sum = k cubed - 3k.
• a + b + c = 0 means a cubed + b cubed + c cubed = 3abc.
• a squared - b squared = (a + b)(a - b).
• a cubed + b cubed = (a + b)(a squared - ab + b squared).

Practice Questions With Answers

1. Find the value of 75 squared - 25 squared.
   Answer: 5,000 (100 x 50).
2. If a + b = 10 and a squared + b squared = 58, find ab.
   Answer: 21 ((100 - 58) / 2).
3. If x - 1/x = 2, find x squared + 1/x squared.
   Answer: 6 (4 + 2).
4. Find the value of (a + b) squared - (a - b) squared for a = 3 and b = 4.
   Answer: 48 (4ab).
5. If x + y = 6 and xy = 8, find x cubed + y cubed.
   Answer: 72 (216 - 3 x 8 x 6).
6. Find the value of 1001 squared.
   Answer: 1,002,001 ((1000 + 1) squared).
7. If a + b = 5 and ab = 6, find a cubed + b cubed.
   Answer: 35 (125 - 3 x 6 x 5).
8. Find the value of 38 squared - 37 squared.
   Answer: 75 (38 + 37).
9. If x squared + 1/x squared = 14 and x is positive, find x + 1/x.
   Answer: 4 (square root of 16).
10. Find the value of (2x + 3)(2x - 3) for x = 4.
    Answer: 55 (64 - 9).

How to Practise This Chapter

1. Learn the formulas in the table until you can write them without looking.
2. Solve the solved examples again on your own, without reading the solution.
3. Attempt the practice questions above with a timer of 10 minutes.
4. Solve the matching SSC algebra practice paper to test yourself in exam style.
5. Check the previous year papers to see how SSC frames this topic.

Related Notes and Practice Papers

• Quadratic Equations Notes
• Surds and Indices Notes
• Square Root and Cube Root Notes
• Simplification and BODMAS Notes
• SSC Algebra Practice Paper

Explore More SSC Subjects

SSC exams test many subjects, so connect this topic with the related subjects below:

• Reasoning Notes
• Statistics Notes
• Indian Economy Notes
• English Notes
• General Awareness Notes
• All SSC subjects and notes

Frequently Asked Questions

What are algebraic identities?

Algebraic identities are equations that are true for all values of the variables, such as (a + b) squared = a squared + 2ab + b squared.

How many questions come from algebra in SSC exams?

Three to five questions come from algebra in SSC CGL Tier 1 and more in Tier 2.

What is the formula for a squared + b squared?

a squared + b squared = (a + b) squared - 2ab = (a - b) squared + 2ab.

What is the trick for x + 1/x?

If x + 1/x = k, then x squared + 1/x squared = k squared - 2 and x cubed + 1/x cubed = k cubed - 3k.

What happens when a + b + c = 0?

Then a cubed + b cubed + c cubed = 3abc.

How do I find the difference of two squares quickly?

Use a squared - b squared = (a + b)(a - b).

Do I need to solve for x in x + 1/x questions?

No. Use the formulas directly because they are faster and give the exact answer.

How should I practise algebra?

Memorise the identities, solve the examples here and attempt the algebra practice paper.