Important Questions for Class 8 Maths Algebraic Expressions and Identities

Important Questions on Algebraic Expressions and Identities for Class 8 are provided in this Maths article to help students build a strong understanding of algebraic concepts. These Class 8 Algebraic Expressions and Identities Important Questions help students practise simplifying expressions and applying algebraic identities effectively. The chapter covers topics such as algebraic expressions, terms, coefficients, factors, and important identities used in solving mathematical problems. Our subject experts have prepared detailed solutions based on the CBSE syllabus and NCERT textbook guidelines. This study material helps students revise important concepts thoroughly and prepare confidently for examinations.

Very Short Answer Questions

1. What is the coefficient of x² in the expression 5x² – 3x + 7?
2. Identify the number of terms in the expression: 4x²y – 4x²y²z² + z²
3. What is a monomial? Give one example.
4. Classify the polynomial: 2y – 3y² + 4y³ (monomial/binomial/trinomial/polynomial)
5. Write the identity: (a + b)²  = ?
6. Write the identity: (a – b)(a + b) = ?
7. What is the product of 4x and 5y?Identify like terms from: 7x, 14x, –13x, 5x², 7y, 7xy
8. Write the identity: (x + a)(x + b) = ?
9. What is the coefficient of xy in 7xy - 5x?

Short Answer Questions

1. Add: 7xy + 5yz – 3zx, 4yz + 9zx – 4y, –3xz + 5x – 2xy. Combine like terms.
2. Subtract 5x² – 4y² + 6y – 3 from 7x² – 4xy + 8y² + 5x – 3y.
3. Find the product of the following pairs of monomials: (i) –4p and 7p (ii) –4p and 7pq (iii) 4p³ and –3p
4. Find the areas of rectangles with the following pairs of monomials as length and breadth: (i) (p, q) (ii) (10m, 5n) (iii) (4x, 3x²)
5. Multiply: 3x × (4p² + 5p + 7). Write each step clearly.
6. Simplify and evaluate: x(x – 3) + 2 for x = 1.
7. Find the product: (a + 7)(b – 5). Are there any like terms?
8. Multiply the binomials: (2x + 5) and (4x – 3).
9. Using Identity I, find: (i) (2x + 3y)² (ii) 103²
10. Using Identity II, find: (i) (4p – 3q)² (ii) (4.9)²

Long Answer Questions

1. Simplify: 3y(2y – 7) – 3(y – 4) – 63 and evaluate for y = –2.
2. Add: 4y(3y² + 5y – 7) and 2(y³ – 4y² + 5). Show all steps.
3. Subtract 3pq(p – q) from 2pq(p + q). Show full working.
4. Multiply (a + b)(2a – 3b + c) – (2a – 3b)c and simplify completely.
5. Simplify using identities: (i) (x² – 5)(x + 5) + 25 (ii) (a + b)(c – d) + (a – b)(c + d) + 2(ac + bd) (iii) (x + y)(x² – xy + y²)
6. Using Identity III, find: (i) 983² – 17² (ii) 194 × 206 (iii) (3m/2 + 2n/3)(3m/2 – 2n/3)
7. Obtain the volume of rectangular boxes with the following length, breadth and height: (i) 5a, 3a², 7a⁴ (ii) 2p, 4q, 8r (iii) xy, 2x²y, 2xy²
8. Using the identity (x + a)(x + b) = x² + (a + b)x + ab, find: (i) 501 × 502 (ii) 95 × 103 (iii) 103 × 104

Application-Based Questions

1. Using identities, evaluate: (i) 71² (ii) 99² (iii) 998² (iv) 297 × 303 (v) 78 × 82
2. Show that (3x + 7)² – 84x = (3x – 7)²
3. Show that (9p – 5q)² + 180pq = (9p + 5q)²
4. Show that (a – b)(a + b) + (b – c)(b + c) + (c – a)(c + a) = 0
5. Using a² – b² = (a + b)(a – b), find: (i) 51² – 49² (ii) (1.02)² – (0.98)² (iii) 153² – 147²
6. The length of a rectangle is (3x + 2) cm and breadth is (2x – 1) cm. Find: (i) Area of the rectangle (ii) Perimeter of the rectangle (iii) Value of area when x = 3
7. If p – q = 4 and pq = 21, find: (i) p + q (ii) p² + q² (iii) (p + q)²

Standard Identities - Quick Reference

Key Concepts to Remember

1. Terms are added to form expressions; terms are formed as products of factors.
2. Monomials = 1 term | Binomials = 2 terms | Trinomials = 3 terms | Polynomials = one or more terms
3. Like terms have the same variables with the same powers (coefficients may differ).
4. When multiplying a polynomial by a monomial, multiply every term in the polynomial by the monomial.
5. An identity is true for ALL values of the variable; an equation is true only for specific values.
6. Identity IV is the general form of Identities I, II, and III.