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Algebraic Expressions

Algebraic Expressions
science Square
Science Square

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)
            _________________________________
            6a⁵ - 12a⁴ – 6a³ + 18a² multiplication by 6a2.

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

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

            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.

Quiz for Algebraic Expressions

Q.1

3x/y, 7xy⁻¹, 19 x/y, all these expressions can be termed as ____________.

a)

Unlike terms

b)

Polynomials

c)

Like terms

d)

None of the above

Q.2

A man travel 2/9th of his journey by car, 4/6th of his journey by bus and for the rest of his journey he opted to walk. If he covered a total distance of y km, what distance did he travel on foot?

a) y/18
b) 2y/9
c) y/3
d) y/9

Q.3

Add the expressions: (i) 5xy + 6x - 24y² (ii) -x +7 xy - 4y² (iii) 5y² + 9x - 4

a) 12xy + 14x - 28y² -4
b) 12xy + 16x -28y² -4
c) 12xy + 16x -20y² -4
d) none of the above

Q.4

Take away 5x - y² from 8y - 6y² + xy

a) 8y - 7y² -xy
b) 8y - 5y² +xy - 5x
c) 8y - 7y² -xy + 5x
d) 8y + 5y² +xy - 5x

Q.5

What is 35% of 4y/7?

a)

y/5

b)

4y/7

c)

7y/20

d)

none of the above

Q.6

Find the sum: (i) 7a² - 5a + 2 (ii) 3a² - 7 (iii) 2a + 9 (iv) 1 + 2a - 5a²

a) a² - 5a + 1
b) a² - 5a + 5
c) 5a² - 5a + 1
d) 5a² - a + 5

Q.7

Find the sum: 2.5a + 4.7a - 3.2a - 5.8a + a

a) 1.8a
b) -1.8a
c) -0.8a
d) 0.8a

Q.8

Simplify: 3 5/6 ab - 1 2/3 ab - 2ab + 3 1/2 ab

a) 11/5 ab
b) 11/3 ab
c) 11/6 ab
d) 3/11 ab

Q.9

Simplify: 5x⁴ - 7x² + 8x - 1 + 3x³ - 9x² + 7 - 3x⁴ + 11x - 2 + 8x²

a) 2x⁴ + 3x³ - 8x² + 19x + 4
b) 2x⁴ + 3x³ - 8x² - 19x + 4
c) 2x⁴ - x³ - 8x² + 19x + 4
d) none of the above

Q.10

Subtract x³ - y³ +2 from x³ + y³ + 3xy + 1

a) 2y³ - x³ +3 xy - 1
b) 2y³ + x³ - 1
c) 2y³ - x³ +3 xy + 1
d) 2y³ + 3 xy - 1

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