Class 8 Maths – Chapter 9

Algebraic Expressions & Identities

STEP 5: Worksheet – FULL ANSWERS (Step-by-Step)

🟦 Section A: Very Short Answer – Answers

1. An example of an algebraic expression with two terms is 3x + 5.
2. The coefficient of x in 5x − 7 is 5.
3. The expression 2a + 3b − 4 has 3 terms.
4. The constant term in 6y² − 9 is −9.
5. The identity is: (a + b)² = a² + 2ab + b².

🟩 Section B: Short Answer – Answers

1. Expression: 4x² − 3x + 5
   Terms: 4x², −3x, 5
   Coefficients: 4 (of x²), −3 (of x)
2. The identity is:
   (x − y)² = x² − 2xy + y²
3. Given: a = 2, b = 3
   (a + b)² = (2 + 3)² = 5² = 25
4. (x + 5)² = x² + 2(x)(5) + 5²
   = x² + 10x + 25

🟧 Section C: Long Answer – Answers

1. (i) (3x + 2)²
   = (3x)² + 2(3x)(2) + 2²
   = 9x² + 12x + 4
   
   (ii) (5a − 4b)²
   = (5a)² − 2(5a)(4b) + (4b)²
   = 25a² − 40ab + 16b²
2. Verification:
   LHS = (x + y)(x − y)
   = x² − y²
   RHS = x² − y²
   LHS = RHS ✔ Verified

🟥 Section D: Challenge – Answers

1. Given: a + b = 10, ab = 21
   a² + b² = (a + b)² − 2ab
   = 10² − 2(21)
   = 100 − 42
   = 58
2. (2x + 3)(2x − 3)
   = (2x)² − 3²
   = 4x² − 9