Difference of squares: Class 8 practice
a² − b² = (a − b)(a + b). Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Squares
- Algebraic identities
The idea behind difference of squares
a² − b² = (a − b)(a + b). Look for two perfect squares separated by a minus sign; take out a common factor first if there is one.
Step-by-step method
- Take out any common factor.
- Write each term as a square.
- Use (a − b)(a + b).
Worked example 1 (Basic)
Factorise x² − 9.
- = (x − 3)(x + 3)
- Answer: (x − 3)(x + 3)
Worked example 2 (Standard)
Use a² − b² to evaluate 19² − 10².
- (19 − 10)(19 + 10) = 9 × 29
- = 261
- Answer: 261
Worked example 3 (Challenge)
Factorise 192x² − 192.
- Common factor 3: 3(64x² − 64)
- = 3(8x − 8)(8x + 8)
- Answer: 3(8x − 8)(8x + 8)
Common mistakes and misconceptions
- Using it for a sum of squares
- Forgetting the common factor
Practice questions
- (Basic) Factorise 25x² − 4.
- (Basic) Factorise 81x² − 4.
- (Standard) Use a² − b² to evaluate 31² − 1².
- (Standard) Use a² − b² to evaluate 17² − 1².
- (Challenge) Factorise 128x² − 72.
- (Challenge) Factorise 243x² − 432.
Answer key with full working
- Q1: = (5x − 2)(5x + 2) → Answer: (5x − 2)(5x + 2)
- Q2: = (9x − 2)(9x + 2) → Answer: (9x − 2)(9x + 2)
- Q3: (31 − 1)(31 + 1) = 30 × 32 → = 960 → Answer: 960
- Q4: (17 − 1)(17 + 1) = 16 × 18 → = 288 → Answer: 288
- Q5: Common factor 2: 2(64x² − 36) → = 2(8x − 6)(8x + 6) → Answer: 2(8x − 6)(8x + 6)
- Q6: Common factor 3: 3(81x² − 144) → = 3(9x − 12)(9x + 12) → Answer: 3(9x − 12)(9x + 12)
Syllabus note
This skill is listed under "Factorisation" for Class 8 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is difference of squares in?
"Factorisation", Class 8 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.