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About Algebraic Expressions & Identities — Class 8 CBSE

Multiply polynomials, apply standard algebraic identities, and simplify expressions. This topic is part of the CBSE Class 8 mathematics syllabus (chapter: Chapter 6). On this page you can practice 64 questions across three difficulty levels — 20 easy, 24 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 39-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Algebraic Expressions & Identities

  • Introduction to Algebraic Expressions
  • Operations on Algebraic Expressions
  • Introduction to Standard Identities
  • Applying Identities and Fourth Identity
  • Factorization Using Identities & Summary

Interactive lesson · about 15 minutes · checkpoint question after every unit

Algebraic Expressions & Identities — solved examples for Class 8 CBSE

Example 1easy

Ravi identified the terms in the expression 5xy - 3y + 7xz as 5xy, 3y, and 7xz. He stated that the coefficient of y in -3y is 3. What error did Ravi make?
  1. A)He incorrectly identified the terms.
  2. B)He incorrectly identified the coefficient of y.
  3. C)Both A and B are incorrect.
  4. D)Ravi made no error.

Step-by-step solution

  1. The terms in the expression 5xy - 3y + 7xz are 5xy, -3y, and 7xz. Ravi correctly identified these terms (ignoring the sign for 3y in his list, but implicitly including it in the original expression).
  2. The coefficient is the numerical factor of a term. For the term -3y, the numerical factor is -3, not 3. Ravi made an error in identifying the coefficient of y.

Answer: He incorrectly identified the coefficient of y.

Example 2medium

Identify the coefficient of xy in the expression 5x²y - 3xy² + 7xy - 6x + 2y - 9. Then find the degree of the term -3xy².
  1. A)7, 2
  2. B)7, 3
  3. C)-3, 2
  4. D)-3, 3

Step-by-step solution

  1. The term containing 'xy' is 7xy. The coefficient of xy is 7.
  2. The term is -3xy². The variables are x (power 1) and y (power 2).
  3. The sum of the powers of the variables in -3xy² is 1 + 2 = 3.
  4. So, the degree of the term -3xy² is 3.

Answer: 7, 3

Example 3hard

Simplify the expression: (2x - 3y)(3x + 4y) - (x - 2y)²
  1. A)5x² + 19xy - 13y²
  2. B)5x² - 19xy + 13y²
  3. C)5x² + 19xy + 13y²
  4. D)5x² - 19xy - 13y²

Step-by-step solution

  1. Expand the first product: (2x - 3y)(3x + 4y) = 2x(3x + 4y) - 3y(3x + 4y) = 6x² + 8xy - 9xy - 12y² = 6x² - xy - 12y²
  2. Expand the second term using the identity (a - b)² = a² - 2ab + b²: (x - 2y)² = x² - 2(x)(2y) + (2y)² = x² - 4xy + 4y²
  3. Subtract the second expanded expression from the first: (6x² - xy - 12y²) - (x² - 4xy + 4y²)
  4. Distribute the negative sign and combine like terms: 6x² - xy - 12y² - x² + 4xy - 4y² = (6x² - x²) + (-xy + 4xy) + (-12y² - 4y²) = 5x² + 3xy - 16y²

Answer: 5x² + 19xy - 13y²

Practice questions on Algebraic Expressions & Identities

  1. Q1.easy

    Which of the following statements about algebraic expressions is TRUE?
    1. A)4x - 5y + 3 is a monomial.
    2. B)7p²q is a binomial.
    3. C)x² + y² is a binomial.
    4. D)A polynomial can have terms with negative exponents.
    Show answer

    Answer: x² + y² is a binomial.

    Hint: Recall the definitions of monomial, binomial, and polynomial based on the number of terms and the nature of exponents.

  2. Q2.easy

    A student simplified (7x - 4y) - (3x - 2y) as 7x - 4y - 3x - 2y. What mistake did the student make?
    1. A)Incorrectly combining x terms.
    2. B)Incorrectly combining y terms.
    3. C)Incorrectly distributing the negative sign.
    4. D)There is no mistake.
    Show answer

    Answer: Incorrectly distributing the negative sign.

    Hint: When removing parentheses preceded by a minus sign, remember to change the sign of every term inside the parentheses.

  3. Q3.easy

    When multiplying a monomial by a polynomial, which property is primarily used?
    1. A)Commutative property
    2. B)Associative property
    3. C)Distributive property
    4. D)Identity property
    Show answer

    Answer: Distributive property

    Hint: Consider how a term outside a parenthesis multiplies each term inside the parenthesis.

  4. Q4.medium

    Simplify the expression: (4a - 3b + 2c) - (2a + 5b - c) + (-a + b + 3c)
    1. A)a - 7b + 6c
    2. B)a - 9b + 4c
    3. C)a - 7b + 4c
    4. D)3a - 7b + 6c
    Show answer

    Answer: a - 7b + 6c

    Hint: Carefully distribute the negative signs when removing parentheses and then combine like terms.

  5. Q5.medium

    Ravi is calculating the area of a rectangular garden. The length of the garden is (3x + 2y) meters and the breadth is 5x meters. If x = 2 and y = 1, what is the area of the garden?
    1. A)80 square meters
    2. B)100 square meters
    3. C)120 square meters
    4. D)140 square meters
    Show answer

    Answer: 80 square meters

    Hint: First, write an algebraic expression for the area, then substitute the given values of x and y.

  6. Q6.medium

    What is the product of (7p - 5q) and (2p + 3q)?
    1. A)14p² - pq - 15q²
    2. B)14p² + 11pq - 15q²
    3. C)14p² + 31pq - 15q²
    4. D)14p² - 31pq - 15q²
    Show answer

    Answer: 14p² + 11pq - 15q²

    Hint: Use the distributive property (FOIL method) to multiply each term in the first binomial by each term in the second binomial.

  7. Q7.hard

    Evaluate (101.5)² - (98.5)² using a suitable algebraic identity.
    1. A)500
    2. B)550
    3. C)600
    4. D)609
    Show answer

    Answer: 600

    Hint: Recognize the form a² - b² and recall the identity that simplifies it into a product of two terms.

  8. Q8.hard

    If 9x² + kx + 16y² is a perfect square, what is the possible value of k?
    1. A)12
    2. B)24
    3. C)36
    4. D)48
    Show answer

    Answer: 24

    Hint: A perfect square trinomial is of the form (a + b)² = a² + 2ab + b² or (a - b)² = a² - 2ab + b². Match the given expression with one of these forms.

  9. Q9.hard

    Which of the following statements is NOT always true for all real values of a and b?
    1. A)(a + b)² = a² + 2ab + b²
    2. B)(a - b)² = a² - 2ab + b²
    3. C)a² - b² = (a - b)(a + b)
    4. D)(a + b)² = a² + b²
    Show answer

    Answer: (a + b)² = a² + b²

    Hint: Carefully recall the standard algebraic identities. One of the options represents a common mistake or a specific case, not a general truth.

These are 9 of the 64 questions available for Algebraic Expressions & Identities. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.