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About Algebraic Expressions — Class 8 ICSE

Work with polynomials, perform operations on algebraic expressions, and learn identities. This topic is part of the ICSE Class 8 mathematics syllabus (chapter: Chapter 5). On this page you can practice 54 questions across three difficulty levels — 20 easy, 20 medium, and 14 hard — each with a visual step-by-step solution, plus a timed 31-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Algebraic Expressions

  • Introduction to Algebraic Expressions
  • Operations on Algebraic Expressions: Addition and Subtraction
  • Operations on Algebraic Expressions: Multiplication
  • Introduction to Algebraic Identities and Division Basics
  • Summary, Connections, and Exam Preparation

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

Algebraic Expressions — solved examples for Class 8 ICSE

Example 1easy

Consider the algebraic expression 7x²y - 5xy + 3. Which of the following statements is TRUE?
  1. A)The expression has 2 terms.
  2. B)The coefficient of xy is 5.
  3. C)The constant term is 3.
  4. D)The variable in the first term is x.

Step-by-step solution

  1. An algebraic expression is made up of terms separated by + or - signs. The given expression 7x²y - 5xy + 3 has three terms: 7x²y, -5xy, and 3. So, option A is false.
  2. The coefficient of a term is the numerical factor of that term. In -5xy, the coefficient of xy is -5 (including the sign). So, option B is false.
  3. A constant term is a term in an algebraic expression that has a value that is fixed and does not contain any variables. In the expression, 3 is the constant term. So, option C is true.
  4. The variables in the first term 7x²y are x and y. So, option D is false.

Answer: The constant term is 3.

Example 2medium

Which of the following statements is TRUE about the algebraic expression 9x³y² - 4xy⁴ + 7x² - 12?
  1. A)The degree of the expression is 4.
  2. B)It is a binomial expression.
  3. C)The coefficient of xy⁴ is 4.
  4. D)It is a polynomial with degree 5.

Step-by-step solution

  1. Identify the degree of each term: 9x³y² has degree 3+2=5. -4xy⁴ has degree 1+4=5. 7x² has degree 2. -12 (constant) has degree 0.
  2. The degree of the polynomial is the highest degree among its terms, which is 5.
  3. The expression has 4 terms (9x³y², -4xy⁴, 7x², -12), so it is not a binomial. The coefficient of xy⁴ is -4, not 4.
  4. Therefore, the statement 'It is a polynomial with degree 5' is true.

Answer: It is a polynomial with degree 5.

Example 3hard

If P(x) = (3x² - 5x + 7) - (2x² + 4x - 1) and Q(x) = x(x - 9), what is the degree of the expression P(x) + Q(x)?
  1. A)1
  2. B)2
  3. C)3
  4. D)0

Step-by-step solution

  1. Simplify P(x): P(x) = 3x² - 5x + 7 - 2x² - 4x + 1 = (3x² - 2x²) + (-5x - 4x) + (7 + 1) = x² - 9x + 8.
  2. Simplify Q(x): Q(x) = x(x - 9) = x² - 9x.
  3. Add P(x) and Q(x): P(x) + Q(x) = (x² - 9x + 8) + (x² - 9x) = 2x² - 18x + 8.
  4. The highest power of x in the resulting expression is 2. Therefore, the degree of P(x) + Q(x) is 2.

Answer: 2

Practice questions on Algebraic Expressions

  1. Q1.easy

    Which of the following groups contains only like terms?
    1. A)3x, 3y, 3z
    2. B)5p², -2p², 7p²
    3. C)4ab, 4a, 4b
    4. D)6mn, -2m, 3n
    Show answer

    Answer: 5p², -2p², 7p²

    Hint: Like terms have the same variables raised to the same powers.

  2. Q2.easy

    Rohan was asked to simplify the expression (5x + 3y) - (2x - 4y). His solution steps are given below:
    Step 1: 5x + 3y - 2x - 4y
    Step 2: (5x - 2x) + (3y - 4y)
    Step 3: 3x - y
    Where did Rohan make a mistake?
    1. A)Step 1: He incorrectly distributed the negative sign.
    2. B)Step 2: He incorrectly grouped the like terms.
    3. C)Step 3: He incorrectly combined the like terms.
    4. D)Rohan's solution is correct, there is no mistake.
    Show answer

    Answer: Step 1: He incorrectly distributed the negative sign.

    Hint: Pay close attention to how the negative sign outside the parenthesis affects the terms inside when removing the parenthesis.

  3. Q3.easy

    What is the degree of the polynomial 8x³y² - 5x²y⁵ + 9x⁴?
    1. A)3
    2. B)4
    3. C)5
    4. D)7
    Show answer

    Answer: 7

    Hint: The degree of a polynomial is the highest sum of the powers of variables in any single term.

  4. Q4.medium

    What is the sum of the polynomials (5a²b - 3ab + 6) and (-2a²b + 7ab - 8)?
    1. A)3a²b + 4ab - 2
    2. B)7a²b - 10ab + 14
    3. C)3a²b - 10ab + 2
    4. D)7a²b + 4ab - 2
    Show answer

    Answer: 3a²b + 4ab - 2

    Hint: To add polynomials, group the like terms together and then combine their coefficients. Pay close attention to the signs.

  5. Q5.medium

    Subtract (3x²y - 5xy + 2y²) from (7x²y + 2xy - 4y²).
    1. A)4x²y + 7xy - 6y²
    2. B)4x²y - 3xy - 2y²
    3. C)-4x²y - 7xy + 6y²
    4. D)10x²y - 3xy - 2y²
    Show answer

    Answer: 4x²y + 7xy - 6y²

    Hint: Remember that subtracting an expression means adding its additive inverse. Change the sign of each term in the expression being subtracted before combining like terms.

  6. Q6.medium

    Simplify the expression: 4x(3x² - 5x + 2)
    1. A)12x² - 20x + 8x
    2. B)12x³ - 20x² + 8x
    3. C)12x³ - 5x + 2
    4. D)4x³ - 20x² + 8x
    Show answer

    Answer: 12x³ - 20x² + 8x

    Hint: Use the distributive property. Multiply the monomial outside the parenthesis by each term inside the parenthesis.

  7. Q7.hard

    Simplify the expression: 3x² - [5y² - {2x² - (3y² - 4x²)}] - 6xy.
    1. A)9x² - 8y² - 6xy
    2. B)-3x² - 2y² - 6xy
    3. C)9x² - 2y² - 6xy
    4. D)3x² - 8y² - 6xy
    Show answer

    Answer: 9x² - 2y² - 6xy

    Hint: Work from the innermost brackets outwards. Pay close attention to the signs when removing parentheses and braces.

  8. Q8.hard

    Find the product of (2x² - 3x + 4) and (x - 2).
    1. A)2x³ - 7x² + 10x - 8
    2. B)2x³ - x² + 2x - 8
    3. C)2x³ - 7x² + 2x - 8
    4. D)2x³ - 7x² + 10x + 8
    Show answer

    Answer: 2x³ - 7x² + 10x - 8

    Hint: Multiply each term of the first polynomial by each term of the second polynomial, then combine like terms.

  9. Q9.hard

    Divide (12x⁴y³ - 18x³y⁴ + 24x²y²) by (-6x²y²).
    1. A)-2x²y + 3xy² - 4
    2. B)2x²y - 3xy² + 4
    3. C)-2x²y + 3xy² + 4
    4. D)2x²y - 3xy² - 4
    Show answer

    Answer: -2x²y + 3xy² - 4

    Hint: Divide each term of the polynomial by the monomial. Remember the rules for dividing exponents and handling signs.

These are 9 of the 54 questions available for Algebraic Expressions. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.