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Algebraic Expressions and Identities (Ch.8) Practice Problems with Solutions - CBSE Grade 8

CBSE Grade 8 | Chapter 8: Algebraic Expressions and Identities
Name: _________________________ Date: _________________________ Score: _______ / 40

3x² − 2x + 5 is a trinomial and the coefficient of y in 5xy − 3y + 2 is −3, so classifying terms and reading off coefficients open this Grade 8 sheet. Multiplying (a + b)² gives a² + 2ab + b²; the key also holds (x − 3)(x + 3) = x² − 9.

Key Takeaways

Section A: Multiple Choice Questions (1 Mark Each)

Choose the correct option for each question.
1. The expression 3x² − 2x + 5 is a:
(a) Monomial(b) Binomial(c) Trinomial(d) Polynomial with 4 terms
2. The coefficient of y in 5xy − 3y + 2 is:
(a) 5x(b) −3(c) 5x − 3(d) 2
3. (a + b)² = ?
(a) a² + b²(b) a² + 2ab + b²(c) a² − 2ab + b²(d) 2a + 2b
4. The product of (x + 3)(x − 3) is:
(a) x² − 9(b) x² + 9(c) x² − 6x + 9(d) x² + 6x − 9
5. What is the value of (102)² using identity?
(a) 10,000(b) 10,204(c) 10,404(d) 10,604
6. The like term of 5x²y is:
(a) 3x²y(b) 5xy²(c) 3x²y²(d) 5x²y²

Section B: Short Answer Type Questions (2 Marks Each)

Show all steps clearly.
7. Add: 5x² − 3x + 2 and −2x² + 7x − 5.
8. Subtract: 3a² + 5ab − 2b² from 8a² − 3ab + 4b².
9. Find the product: (2x + 5)(3x − 2).
10. Simplify using identity: (3x + 4y)(3x − 4y).
11. Evaluate 97² using a suitable identity.
12. Find the value of x² + y² if x + y = 9 and xy = 20.
13. Multiply: (a − 2b)(a² + 2ab + 4b²).
14. Simplify: (2x + 3)² − (2x − 3)².

Section C: Word Problems (3 Marks Each)

Apply the concepts to solve real-life problems.
15. The length of a rectangle is (2x + 3) cm and breadth is (x − 1) cm. Find the area in terms of x.
16. A square has side (3y − 2) cm. Find its area using identity.
17. The product of two consecutive odd numbers is 143. If they are (2n+1) and (2n+3), find n.
18. Find the volume of a cuboid with dimensions (x + 2), (x − 1), and (x + 3) in terms of x.
19. Rohan bought (3p + 2) kg of apples at ₹(p − 1) per kg. Find the total cost in terms of p.
20. The sum of two numbers is 25 and the sum of their squares is 313. Find the product of the numbers.

Answer Key

1. c) Trinomial
2. b) −3
3. b) a² + 2ab + b²
4. a) x² − 9
5. c) 10,404
6. a) 3x²y
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
13. Refer to solution guide.
14. Refer to solution guide.
15. Refer to solution guide.
16. Refer to solution guide.
17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet

People Also Ask

What type of expression is 3x² − 2x + 5?

A trinomial, option (c) in this worksheet (Q1).

What is the coefficient of y in 5xy − 3y + 2?

−3, option (b) in this worksheet (Q2).

What does (a + b)² expand to?

a² + 2ab + b².

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