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ICSE-VIII-Mathematics

12: Algebraic Identities Class 8 Maths

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    Section : A
  • Qstn #1
    Use direct method to evaluate the following products :
  • #1-i
    (x + 8)(x + 3)
    Ans : (x + 8)(x + 3) = (x × x) + (x × 3) + (8 × x) + (8 × 3)
    = x2 + 3x + 8x + 24
    = x2 + 11x + 24
  • #1-ii
    (y + 5)(y - 3)
    Ans : (y + 5)(y - 3) = (y × y) + (y × -3) + (5 × y) + (5 × -3)
    = y2 + (-3y) + (5y) - 15
    = y2 - 3y + 5y - 15
    = y2 + 2y - 15
  • #1-iii
    (a - 8)(a + 2)
    Ans : (a - 8)(a + 2) = (a × a) + (a × 2) + (-8) × a + (-8)(2)
    = a2 + 2a - 8a - 16
    = a2 - 6a - 16
  • #1-iv
    (b - 3)(b - 5)
    Ans : (b - 3)(b - 5) = (b × b) + (b × -5) + (-3) × b + (-3)(-5)
    = b2 - 5b - 3b + 15
    = b2 - 8b + 15
  • #1-v
    (3x - 2y)(2x + y)
    Ans : (3x - 2y)(2x + y) = (3x × 2x) + (3x × y) + (-2y × 2x) + (-2y × y)
    = 6x2 + 3xy - 4xy -2y2
    = 6x2 - xy - 2y2
  • #1-vi
    (5a + 16)(3a - 7)
    Ans : (5a + 16)(3a - 7) = (5a × 3a) + (5a × -7) + (16 × 3a) + 16 × -7
    = 15a2 + (-35a) + 48a + (-112)
    = 15a2 - 35a + 48a - 112
    = 15a2 + 13a - 112
  • #1-vii
    (8 - b) (3 + b)
    Ans : (8 - b)(3 + b) = (8 × 3) + (8 × b) + (-b × 3) + (-b × b)
    = 24 + 8b - 3b - b2
    = 24 + 5b - b2
  • Qstn #2
    Use direct method to evaluate :
    Ans : Note: (a + b)(a - b) = a2 - b2
  • #2-i
    (x + 1) (x - 1)
    Ans : (x + 1)(x - 1)= (x)2 - (1)2
    = x2 - 1
  • #2-ii
    (2 + a)(2 - a)
    Ans : (2 + a)/(2 - a)= (2)2 -
    (a)2
    = 4 - a2
  • #2-iii
    (3b - 1)(3b + 1)
    Ans : (3b - 1)(3b + 1) = (3b)2 - (1)2
    = 9b2 - 1
  • #2-iv
    (4 + 5x)(4 - 5x)
    Ans : (4 + 5x)(4 - 5x)
    = (4)2 - (5x)2
    = 16 - 25x2
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