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Q1. For what value of a and b, the algebraic expression a3 + b3 - 3ab(a + b) equals 37.
  • 1) a = 1; b = -2
  • 2) a = -1; b = 1
  • 3) a = -2; b = 3
  • 4) a = 2; b = -3

Solution

Substituting the values of a and b from each of the given options, we get (-2)3 + (3)3 - 3 × (-2) × 3(-2 + 3) = -8 + 27 + 18 = 37. Hence, the value of a = -2 and b = 3 satisfies the equation : a3 + b3 -3ab(a + b)
Q2. Which of the following is not a factor of any term of the algebraic expression 17x2y - 12xy + 13y3 - 7xyz?
  • 1) 2
  • 2) x2
  • 3) y2
  • 4) 13x2y

Solution

Looking at all the options, the first 3 options can divide one or the other term of the expression, only the last option does not divide any of the term of the given algebraic expression.
Q3. Classify the following as monomial, binomial or trinomial: (i) 2x + 3y (ii) 2x3 + 3y2 - 1 (iii) 2xy + 10 (iv) -9x4yz

Solution

(i) 2x + 3y : Binomial (ii) 2x3 + 3y2 - 1 : Trinomial (iii) 2xy + 10 : Binomial (iv) -9x4yz : Monomial
Q4. x2 - 2x + 3 - A = -3x2 + 4x - 9, then A =
  • 1) 4x2 - 6x + 12
  • 2) -4x2 - 6x + 12
  • 3) 4x2 + 6x + 12
  • 4) 4x2 + 6x - 12

Solution

x2 - 2x + 3 - A = -3x2 + 4x - 9 Thus, -A = -3x2 + 4x - 9 - (x2 - 2x + 3) -A = -3x2 + 4x - 9 - x2 + 2x - 3 -A = -4x2 + 6x - 12 Hence, A = 4x2 - 6x + 12
Q5. Simplify: 20x - [15x3 + 5x2 - {8x2 - (4 - 2x - x3) - 5x3} - 2x].

Solution

Consider:
Q6. Find the value of expression (x + y)2 - (x - y)2, if .

Solution

(x + y)2 - (x - y)2 = x2 + y2 + 2xy - (x2 + y2 - 2xy) = 4xy Putting we get (x + y)2 - (x - y)2 = 
Q7. From the sum of 4x + y and 3x - 5y, subtract the sum of -6x + 2y and 7x - 5y.

Solution

We have to find: [(4x + y) + (3x - 5y)] - [(-6x + 2y) + (7x - 5y)] = [4x + y + 3x - 5y] - [-6x + 2y + 7x - 5y] = (7x - 4y) - (x - 3y) = 7x - 4y - x + 3y = 6x - y


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