1. Simplify 3x + 4x − 2x.
- A5x
- B9x
- C5x²
- Dx
Show answer
Answer: A) 5x
All like terms (in x). 3 + 4 − 2 = 5. Result: 5x.
Class 8 Algebraic Expressions and Identities — practice questions with answers
Algebra · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
2. Expand: (5m − 4n)(5m + 4n).
- A25m² − 16n²
- B25m² + 16n²
- C25m² − 40mn − 16n²
- D5m² − 16n²
Show answer
Answer: A) 25m² − 16n²
(a−b)(a+b) = a² − b² with a = 5m, b = 4n: (5m)² − (4n)² = 25m² − 16n².
3. Subtract the sum of (2x² − 3x) and (x² + 5x) from 6x² + 4x.
- A3x² + 2x
- B3x² + 12x
- C9x² + 6x
- D3x² − 2x
Show answer
Answer: A) 3x² + 2x
Sum = (2x²−3x)+(x²+5x) = 3x² + 2x. Then (6x²+4x) − (3x²+2x) = 3x² + 2x.
4. For which value of k is x² + 14x + k a perfect square?
- A49
- B7
- C14
- D196
Show answer
Answer: A) 49
A perfect square looks like (x + b)² = x² + 2bx + b². Matching 2b = 14 gives b = 7, so k = b² = 49 and x² + 14x + 49 = (x + 7)². Stopping at b = 7 gives 7; squaring 14 instead of 7 gives 196.
5. Neha writes (2x + 3)² = 4x² + 9. Substituting x = 1 into both sides, what does the check show?
- ABoth sides give 13, so Neha is correct
- BLeft side is 25 but right side is 13 — the middle term 12x is missing
- CLeft side is 13 but right side is 25 — the 3 should not be squared
- DLeft side is 25 and right side is 25, so the check proves nothing
Show answer
Answer: B) Left side is 25 but right side is 13 — the middle term 12x is missing
At x = 1 the left side is (2 + 3)² = 25, while Neha's right side gives 4 + 9 = 13. The sides disagree, so her expansion is wrong. The correct one is (2x + 3)² = 4x² + 2(2x)(3) + 9 = 4x² + 12x + 9, which at x = 1 gives 4 + 12 + 9 = 25 and matches. (a + b)² always carries a middle term.
Practise all 90 questions free →
10 free questions a day without an account — unlimited with a free account.