Class 8 Maths – Chapter 9

Algebraic Expressions & Identities

STEP 6: Important Exam Questions (Solved)

🟦 Very Short Answer Questions (1 Mark)

1. Write the identity for (a + b)².
   Answer: (a + b)² = a² + 2ab + b²
2. How many terms are there in 4x² − 3x + 7?
   Answer: There are 3 terms.
3. What is the coefficient of y in 9y − 5?
   Answer: 9
4. Is x² − y² an identity?
   Answer: Yes

🟩 Short Answer Questions (2–3 Marks)

1. Expand: (x + 4)²
   Solution:
   (x + 4)² = x² + 2(x)(4) + 4²
   = x² + 8x + 16
2. Write three algebraic expressions with one term, two terms and three terms.
   Answer:
   One term: 5x
   Two terms: x + 2
   Three terms: x² + 3x − 4
3. Find the value of (a − b)² when a = 5 and b = 2.
   Solution:
   (5 − 2)² = 3² = 9

🟧 Long Answer Questions (4–5 Marks)

1. Expand and simplify: (2x + 3)²
   Solution:
   (2x + 3)² = (2x)² + 2(2x)(3) + 3²
   = 4x² + 12x + 9
2. Verify: (a + b)(a − b) = a² − b²
   Solution:
   LHS = (a + b)(a − b)
   = a² − b²
   RHS = a² − b²
   Hence, LHS = RHS ✔
3. If a + b = 7 and ab = 10, find a² + b².
   Solution:
   a² + b² = (a + b)² − 2ab
   = 7² − 2(10)
   = 49 − 20
   = 29

📝 Examiner Tip

• Always write the identity first.
• Show step-by-step expansion.
• Do not skip middle steps.
• Use proper brackets.