Chapter 11 · ICSE Class 8 Mathematics

Algebraic Expressions (Including Operations on Algebraic Expressions)

Multiply and divide algebraic expressions with multiple terms, building on the like-terms work from before.

🔤 Chapter 11

Grouping like terms in the expression 3x plus 5y minus x plus 2y The expression 3x + 5y - x + 2y with the x-terms highlighted in one color and the y-terms highlighted in another, showing how to group like terms before simplifying to 2x + 7y 3x + 5y − x + 2y Group like terms together 2x + 7y
11.1

Multiplying Algebraic Expressions

To multiply a monomial by a polynomial, multiply the monomial by every term inside. To multiply two binomials, multiply each term in the first by each term in the second, then combine like terms.

1

Multiply: 3x(2x + 5)

6x² + 15x

2

Multiply: (x + 3)(x + 4)

x² + 4x + 3x + 12 = x² + 7x + 12

11.2

Dividing Algebraic Expressions

To divide a polynomial by a monomial, divide each term of the polynomial by the monomial separately, simplifying the coefficients and subtracting exponents on matching variables.

1

Divide: (12x³ + 8x²) ÷ 4x

3x² + 2x

2

Divide: (15a²b − 10ab²) ÷ 5ab

3a − 2b

Practice

Exercises

1. Multiply: 4y(3y − 2)

2. Multiply: (x + 2)(x + 5)

3. Multiply: (x − 3)(x + 3)

4. Divide: (20x⁴ − 15x³) ÷ 5x

5. Divide: (18a³b² + 12a²b) ÷ 6a²b

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