Algebraic expressions are mathematical expressions that consists of numbers, variables and mathematical operators.

Maths class 8 Algebraic expression and identities

Terms, factors and coefficients

  • Factors: If algebraic expressions are expressed as the product of numbers, variables or expressions, then each of these numbers and expressions is called the factor of algebraic expressions.

  • Maths class 8 Algebraic expression and identities

    Monomials, Binomials, & Polynomials

    Maths class 8 Algebraic expression and identities

    Like & Unlike terms

    Maths class 8 Algebraic expression and identities

    Addition & Subtraction of Algebraic Expressions

    • Maths class 8 Algebraic expression and identities

      • Maths class 8 Algebraic expression and identities

        • Maths class 8 Algebraic expression and identities

          Multiplication of algebraic expressions

          • Maths class 8 Algebraic expression and identities

            • Product of two monomials = (product of their numerical coefficients) × (product of their variable parts)

            Example 1: 1ab and -2a²b³

            SOLUTION: (1ab) × (-2a²b³)

            = {1 × (-2)} × {ab × a²b³}

            = -2 x a1+2 x b1+3

            = -2a³b⁴.

            • Multiplying a polynomial by a polynomial:

              Suppose (x + y) and (p + q) are two polynomials. By using the distributive property of multiplication over addition twice, we may find their product as given below.

              EXAMPLE 3: Multiply (1a³ – 2a² – a + 3) by (4 – 5a + 6a2)

            SOLUTION: Arranging the terms of the given polynomials in descending power of a and then multiplying:

            1a³ – 2a² – a + 3

            × (4 – 5a + 6a²)
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            6a⁵ - 12a⁴ – 6a³ + 18a² multiplication by 6a2.

            - 5a⁴ + 10a³ + 5a² – 15a multiplication by -5a.

            + 4a³ – 8a² - 4a + 12 multiplication by 4.
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            6a⁵ – 17a⁴ + 8a³ + 15a² – 19a + 12 multiplication by (4 – 5a + 6a²)
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            Identities and its applications

            • Some standard identities are:

            Maths class 8 Algebraic expression and identities

            EXAMPLE 1: Expand (a – 2b)3 using standard algebraic identities.

            SOLUTION: (a– 2b)3 is of the form (a-b)3 where a = a and b = 2b. So we have,

            (a – 2b)3 = (a)3 – (2b)3– 3(a)(2b)(a – 2b) = a3 – 8b3 – 6a2b + 12ab2 [ANS]

            EXAMPLE 2: Find . Given = 12 and ab=3.

            SOLUTION:

            Practice these questions

            Q1) Multiply the following:
            a) 11x2y and 3 b)12 and 33 c)4 and 6

            Q2) Find the value of when

            Q3) Simplify the following:
            a) (x+2y)(3x+4y) – (5x+6y)(7x+8y) b)(9a+10b)(2x+3y) – (4a+5b)(6c+7d)

            Q4) Find the product of the following using identities:
            a)(8x+9y)(8x-9y) b)(10x+11y+23z)2 c)(45a-6b)3 d)(7a+8b)3

            Q5) Simplify using identities:
            a)121 x 121 – 10012 b)9992 c)1012 d)

            Q6) If , find the value of .

            Q7) Find the value of x if 12x=

            Q8) Tick the pair of like terms:

            Maths class 8 Algebraic expression and identities

            Q9) If , find the value of .

            Recap

            • Algebraic expressions are mathematical expressions that consists of numbers, variables and mathematical operators.
            • If algebraic expressions are expressed as the product of numbers, variables or expressions, then each of these numbers and expressions is called the factor of algebraic expressions.
            • Algebraic expressions which contain one non-zero term only are called monomials.

            Algebraic expressions which contain two non-zero terms are called binomials.