Algebra Play — Class 8 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 8 Mathematics chapter "Algebra Play" — 8 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 8 Mathematics chapter "Algebra Play" — 8 important questions with detailed answers for CBSE board exam pre…
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
NCERT Solutions for Class 8 Mathematics — Algebra Play. Step-by-step answers to all 8 textbook questions from this chapter, written for CBSE board preparation and free to use.
Algebra Play — All 8 Questions Solved
Q1. Simplify: 3x + 5x − 2x
Step 1: Combine like terms (all have variable x).
Step 2: 3x + 5x − 2x = (3 + 5 − 2)x
Step 3: = 6x
Q2. Expand: (x + 3)(x + 2)
Step 1: Use FOIL method (First, Outer, Inner, Last).
Step 2: First: x × x = x²
Step 3: Outer: x × 2 = 2x
Step 4: Inner: 3 × x = 3x
Step 5: Last: 3 × 2 = 6
Step 6: Combine: x² + 2x + 3x + 6 = x² + 5x + 6
Q3. Factorize: x² + 7x + 12
Step 1: We need two numbers that multiply to 12 and add to 7.
Step 2: Those numbers are 3 and 4 (3 × 4 = 12, 3 + 4 = 7).
Step 3: x² + 7x + 12 = (x + 3)(x + 4)
Q4. Solve: 2x + 5 = 13
Step 1: 2x + 5 = 13
Step 2: Subtract 5 from both sides: 2x = 13 − 5
Step 3: 2x = 8
Step 4: Divide both sides by 2: x = 4
Step 5: Check: 2(4) + 5 = 8 + 5 = 13 ✓
Q5. Use the identity (a + b)² = a² + 2ab + b² to expand (x + 4)²
Step 1: (x + 4)² = x² + 2(x)(4) + 4²
Step 2: = x² + 8x + 16
Q6. Factorize: 4x² − 25
Step 1: Recognize this as a difference of squares: a² − b² = (a + b)(a − b)
Step 2: 4x² = (2x)² and 25 = 5²
Step 3: 4x² − 25 = (2x)² − 5² = (2x + 5)(2x − 5)
Q7. Solve: 3x − 7 = x + 5
Step 1: 3x − 7 = x + 5
Step 2: Subtract x from both sides: 2x − 7 = 5
Step 3: Add 7 to both sides: 2x = 12
Step 4: Divide by 2: x = 6
Step 5: Check: 3(6) − 7 = 18 − 7 = 11, and 6 + 5 = 11 ✓
Q8. Simplify: (2a + 3b) − (a − 2b)
Step 1: Distribute the negative sign: 2a + 3b − a + 2b
Step 2: Combine like terms: (2a − a) + (3b + 2b)
Step 3: = a + 5b
Algebra Play — Practice MCQs with Answers
Attempt these 20 multiple-choice questions after working through the solutions above. Each carries the correct option and the reasoning behind it, so a wrong answer tells you which idea to revisit.
MCQ 1. What is the coefficient of `x` in the expression `7x^2 - 5xy + 3x - 8`?
- A. 7
- B. -5
- C. 3
- D. -8
Answer: C. 3 — The coefficient of a term is the numerical factor of that term. In the term `3x`, the numerical factor is `3`.
MCQ 2. Simplify: `(3x + 2y) + (5x - y)`
- A. 8x + y
- B. 8x + 3y
- C. 2x + y
- D. 2x + 3y
Answer: A. 8x + y — Combine like terms: `(3x + 5x) + (2y - y) = 8x + y`.
MCQ 3. Find the product of `4a` and `3a^2b`.
- A. 12a^3b
- B. 7a^3b
- C. 12a^2b
- D. 12ab
Answer: A. 12a^3b — Multiply the numerical coefficients and add the powers of the same variables: `4 * 3 * a^(1+2) * b = 12a^3b`.
MCQ 4. Expand `(x + 3)(x - 5)`.
- A. x^2 - 2x - 15
- B. x^2 + 2x - 15
- C. x^2 - 8x - 15
- D. x^2 + 8x - 15
Answer: A. x^2 - 2x - 15 — Using the distributive property (FOIL method): `x*x + x*(-5) + 3*x + 3*(-5) = x^2 - 5x + 3x - 15 = x^2 - 2x - 15`.
MCQ 5. Which of the following is a like term to `5x^2y`?
- A. 5xy^2
- B. 2x^2y
- C. 3xy
- D. 5x^2
Answer: B. 2x^2y — Like terms have the same variables raised to the same powers. `5x^2y` and `2x^2y` both have `x^2` and `y`.
MCQ 6. Subtract `3a - 4b + 5c` from `5a + 2b - 3c`.
- A. 2a + 6b - 8c
- B. 2a - 6b + 8c
- C. 8a - 2b + 2c
- D. 8a + 6b - 8c
Answer: A. 2a + 6b - 8c — `(5a + 2b - 3c) - (3a - 4b + 5c) = 5a + 2b - 3c - 3a + 4b - 5c = (5a - 3a) + (2b + 4b) + (-3c - 5c) = 2a + 6b - 8c`.
MCQ 7. Expand `(2x + 3)^2`.
- A. 4x^2 + 9
- B. 4x^2 + 12x + 9
- C. 2x^2 + 6x + 9
- D. 4x^2 + 6x + 9
Answer: B. 4x^2 + 12x + 9 — Using the identity `(a+b)^2 = a^2 + 2ab + b^2`, where `a=2x` and `b=3`. So, `(2x)^2 + 2(2x)(3) + 3^2 = 4x^2 + 12x + 9`.
MCQ 8. Simplify `(5p - 2q)^2`.
- A. 25p^2 - 4q^2
- B. 25p^2 - 10pq + 4q^2
- C. 25p^2 - 20pq + 4q^2
- D. 25p^2 + 20pq + 4q^2
Answer: C. 25p^2 - 20pq + 4q^2 — Using the identity `(a-b)^2 = a^2 - 2ab + b^2`, where `a=5p` and `b=2q`. So, `(5p)^2 - 2(5p)(2q) + (2q)^2 = 25p^2 - 20pq + 4q^2`.
MCQ 9. Find the value of `(103)^2 - (97)^2`.
- A. 600
- B. 1200
- C. 60
- D. 1000
Answer: B. 1200 — Using the identity `a^2 - b^2 = (a+b)(a-b)`. Here `a=103` and `b=97`. So, `(103+97)(103-97) = (200)(6) = 1200`.
MCQ 10. Factorize `xy + 2x + 3y + 6`.
- A. (x+3)(y+2)
- B. (x+2)(y+3)
- C. (x+y)(2+3)
- D. (x+6)(y+1)
Answer: A. (x+3)(y+2) — Group terms: `(xy + 2x) + (3y + 6)`. Factor out common terms: `x(y + 2) + 3(y + 2)`. Now factor out the common binomial `(y + 2)`: `(x + 3)(y + 2)`.
MCQ 11. Factorize `6ab + 9b^2`.
- A. 3b(2a + 3b)
- B. 3b(2a + 9b)
- C. 3a(2b + 3b)
- D. 6b(a + 3b)
Answer: A. 3b(2a + 3b) — The greatest common factor of `6ab` and `9b^2` is `3b`. Factoring it out gives `3b(2a + 3b)`.
MCQ 12. Factorize `49x^2 - 64y^2`.
- A. (7x - 8y)^2
- B. (7x + 8y)(7x - 8y)
- C. (7x + 8y)^2
- D. (49x - 64y)(49x + 64y)
Answer: B. (7x + 8y)(7x - 8y) — This is in the form `a^2 - b^2`, where `a = 7x` and `b = 8y`. So, `(7x)^2 - (8y)^2 = (7x + 8y)(7x - 8y)`.
MCQ 13. Divide `(12x^3y^2 - 18x^2y^3)` by `3x^2y^2`.
- A. 4x - 6y
- B. 4x - 6y^2
- C. 3x - 6y
- D. 4x^2y^2 - 6x^2y^3
Answer: A. 4x - 6y — Divide each term of the numerator by the denominator: `(12x^3y^2 / 3x^2y^2) - (18x^2y^3 / 3x^2y^2) = 4x - 6y`.
MCQ 14. Factorize `x^2 + 10x + 24`.
- A. (x+4)(x+6)
- B. (x+3)(x+8)
- C. (x+2)(x+12)
- D. (x-4)(x-6)
Answer: A. (x+4)(x+6) — We need two numbers that multiply to 24 and add up to 10. These numbers are 4 and 6. So, `x^2 + 4x + 6x + 24 = x(x+4) + 6(x+4) = (x+6)(x+4)`.
MCQ 15. If `x = 2` and `y = -1`, find the value of `3x^2 - 2xy + y^2`.
- A. 17
- B. 12
- C. 15
- D. 11
Answer: A. 17 — Substitute `x=2` and `y=-1` into the expression: `3(2)^2 - 2(2)(-1) + (-1)^2 = 3(4) - (-4) + 1 = 12 + 4 + 1 = 17`.
MCQ 16. An expression having only one term is called a:
- A. Binomial
- B. Monomial
- C. Trinomial
- D. Polynomial
Answer: B. Monomial — A monomial is an algebraic expression consisting of only one term, such as `5x`, `3xy`, or `7`.
MCQ 17. Simplify `(a + b)^2 - (a - b)^2`.
- A. 2ab
- B. 4ab
- C. 2a^2 + 2b^2
- D. 0
Answer: B. 4ab — Using identities: `(a^2 + 2ab + b^2) - (a^2 - 2ab + b^2) = a^2 + 2ab + b^2 - a^2 + 2ab - b^2 = 4ab`.
MCQ 18. Factorize `5x^3 - 45x` completely.
- A. 5x(x^2 - 9)
- B. 5x(x - 3)^2
- C. 5x(x - 3)(x + 3)
- D. 5x(x - 9)
Answer: C. 5x(x - 3)(x + 3) — First, factor out the common term `5x`: `5x(x^2 - 9)`. Then, recognize `x^2 - 9` as a difference of squares `(x^2 - 3^2)`. So, `5x(x - 3)(x + 3)`.
MCQ 19. Calculate `(100 - 1)(100 + 1)` without direct multiplication.
- A. 9999
- B. 10000
- C. 9990
- D. 10001
Answer: A. 9999 — Using the identity `(a - b)(a + b) = a^2 - b^2`. Here `a=100` and `b=1`. So, `100^2 - 1^2 = 10000 - 1 = 9999`.
MCQ 20. Multiply `3x` by `(4x - 5y)`.
- A. 12x^2 - 15xy
- B. 12x - 15xy
- C. 12x^2 + 15xy
- D. 7x - 5y
Answer: A. 12x^2 - 15xy — Distribute `3x` to each term inside the parenthesis: `3x * 4x - 3x * 5y = 12x^2 - 15xy`.
How to Use These Solutions
Attempt each question yourself first and only then compare with the worked answer. Marks in the CBSE board exam are awarded for the METHOD as much as the final result, so reproduce the steps rather than memorising the last line. Where a solution states a law, a formula or a definition, learn that wording — examiners look for it.
Related practice for this chapter: chapter MCQs, previous-year questions, revision notes and sample papers.