Using algebraic identities: Class 8 practice
(a + b)² = a² + 2ab + b², (a − b)² = a² − 2ab + b² and (a + b)(a − b) = a² − b² save time in expansion and mental arithmetic.. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Squares
- Multiplying monomials
The idea behind using algebraic identities
(a + b)² = a² + 2ab + b², (a − b)² = a² − 2ab + b² and (a + b)(a − b) = a² − b² save time in expansion and mental arithmetic.
Step-by-step method
- Match the expression to an identity.
- Identify a and b.
- Substitute and simplify.
Worked example 1 (Basic)
Expand (2x + 8)².
- (2x)² + 2(2x)(8) + 8²
- Answer: 4x² + 32x + 64
Worked example 2 (Standard)
Expand (4x − 3)².
- (4x)² − 2(4x)(3) + 3²
- Answer: 16x² − 24x + 9
Worked example 3 (Challenge)
Use an identity to find 102².
- (100 + 2)² = 10000 + 400 + 4
- = 10404
- Answer: 10404
Common mistakes and misconceptions
- (a + b)² = a² + b²
- Sign errors in (a − b)²
Practice questions
- (Basic) Expand (3x + 2)².
- (Basic) Expand (3x + 7)².
- (Standard) Expand (5x − 5)².
- (Standard) Expand (5x − 9)².
- (Challenge) Use an identity to find 97².
- (Challenge) Use an identity to find 93².
Answer key with full working
- Q1: (3x)² + 2(3x)(2) + 2² → Answer: 9x² + 12x + 4
- Q2: (3x)² + 2(3x)(7) + 7² → Answer: 9x² + 42x + 49
- Q3: (5x)² − 2(5x)(5) + 5² → Answer: 25x² − 50x + 25
- Q4: (5x)² − 2(5x)(9) + 9² → Answer: 25x² − 90x + 81
- Q5: (100 − 3)² = 10000 − 600 + 9 → = 9409 → Answer: 9409
- Q6: (100 − 7)² = 10000 − 1400 + 49 → = 8649 → Answer: 8649
Syllabus note
This skill is listed under "Algebraic Expressions and Identities" 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 using algebraic identities in?
"Algebraic Expressions and Identities", 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.