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ICSE-VIII-Mathematics

11: Algebraic Expressions Class 8 Maths

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    Section : A
  • Qstn #1
    Separate the constants and variables from the following :
    -7, 7 + x, 7x + yz, √5, √xy, 3yz/8, 4.5y - 3x, 8 - 5, 8 - 5x, 8x - 5y × p and 3y2z ÷ 4x
    Ans : Clearly constants are :
    -7, √5, 8 - 5
    Variables are: 7 + x, 7x + yz, √xy, 3yz/8, 4.5y - 3x
    8 - 5x, 8x - 5y × p and 3y2z ÷ 4x
  • Qstn #2
    Write the number of terms in each of the following polynomials.
  • #2-i
    5x2 + 3 x ax
    Ans : 5x2 + 3 × ax = 5x2 + 3ax
    ∴ The number of terms in this polynomial = 2
  • #2-ii
    ax ÷ 4 - 7
    Ans : ax ÷ 4 - 7 = ax/4 - 7
    ∴ The number of terms in this polynomial = 2
  • #2-iii
    ax - by + y x z
    Ans : ax - by + y × z = ax - by + yz
    ∴ The number of terms in this polynomial = 3
  • #2-iv
    23 + a x b ÷ 2.
    Ans : 23 + a × b ÷ 2 = 23 + ab/2
    ∴ The number of terms in this polynomial = 2
  • Qstn #3
    Separate monomials, binomials, trinomials and polynomials from the following algebraic expressions :
    8 - 3x, xy2, 3y2 - 5y + 8, 9x - 3x2 + 15x3 - 7, 3x × 5y, 3x ÷ 5y, 2y ÷ 7 + 3x - 7 and 4 - ax2 + bx + y
    Ans : Monomials are : xy2, 3x × 5y, 3x ÷ 5y;
    Binomials are : 8 - 3x
    Trinomials are : 3y2 - 5y + 8, 2y ÷ 7 + 3x - 7
    Polynomials are : 8 - 3x, 3y2 - 5y + 8, 9x - 3x2 + 15x3 - 7, 2y ÷ 7 + 3x - 7, 4 - ax2 + bx + y
  • Qstn #4
    Write the degree of each polynomial given below :
  • #4-i
    xy + 7z
    Ans : degree = 2 (Polynomial is xy + 7z)
  • #4-ii
    x2 - 6x3 + 8
    Ans : degree = 3 (Polynomial is x2 - 6x3 + 8y)
  • #4-iii
    y - 6y2 + 5y8
    Ans : degree = 8 (Polynomial is y - 6y2 + 5y8)
  • #4-iv
    xy + yz2 + zx3
    (vi) x5y7 - 8x3y8 + 10x4y4z4
    Ans : degree = 3 (Polynomial is xyz - 3)
    (v) degree = 4 (Polynomial is xy + yz2 - xz3)
    (vi) degree = 12 (Polynomial is x5y7 - 8x3y8 + 10x4, y4z4)
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