Class 9 Mathematics Chapter 4: Exploring Algebraic Identities — practice questions with answers
Free practice for Class 9 Mathematics, Chapter 4: Exploring Algebraic Identities. Try the solved questions below, then take a free test with instant marking and explanations.
56 questions19 easy, 21 medium, 16 hardNCERT · CBSE · State boards
Sample questions with solutions
Q1. Take three consecutive squares 25, 36, 49. Add the smallest and largest and subtract twice the middle one. What is the result?
Show answer
Answer: 2 (± 0)
Why: 74 − 72 = 2. [p.68]
Why: 74 − 72 = 2. [p.68]
Q2. A square of side (a + b) is split into a square a², a square b² and two rectangles. Which identity does this show?
- (a + b)² = a² + 2ab + b²
- (a + b)² = a² + b²
- a² − b² = (a + b)(a − b)
- (a − b)² = a² − b²
Show answer
Answer: A. (a + b)² = a² + 2ab + b²
Why: The two rectangles each have area ab. [p.69–70]
Why: The two rectangles each have area ab. [p.69–70]
Q3. Use (a + b)² to find 105².
Show answer
Answer: 11025 (± 0)
Why: (100 + 5)² = 10000 + 1000 + 25 = 11025. [p.72]
Why: (100 + 5)² = 10000 + 1000 + 25 = 11025. [p.72]
Q4. Use a² = (a + b)(a − b) + b² to find 55².
Show answer
Answer: 3025 (± 0)
Why: 60 × 50 + 25 = 3025. [p.77]
Why: 60 × 50 + 25 = 3025. [p.77]
Q5. Use (a + b)(a − b) to find 104 × 96.
Show answer
Answer: 9984 (± 0)
Why: 100² − 4² = 10000 − 16 = 9984. [p.89]
Why: 100² − 4² = 10000 − 16 = 9984. [p.89]
Q6. Factorise x² + 4x + 4.
- (x + 2)²
- (x + 4)²
- (x + 1)(x + 4)
- (x − 2)²
Show answer
Answer: A. (x + 2)²
Why: x² + 2(x)(2) + 2². [p.72]
Why: x² + 2(x)(2) + 2². [p.72]
Practise all 56 questions free
Timed test, marked instantly, with the correct answer and explanation for every question and a chapter-wise report.
Start the free testUnderstand it by doing
Try the interactive Maths Lab for Class 9.
Frequently asked questions
How many practice questions are there for Class 9 Mathematics Chapter 4: Exploring Algebraic Identities?
56 questions (19 easy, 21 medium, 16 hard). A few are solved on this page; the free test shows the answer and explanation for every question after you submit.
Is this chapter from the NCERT book?
Yes — it follows the NCERT Class 9 Mathematics syllabus, used by CBSE and many state boards.