31.Factorise.

   i) 169m² - 625n²                   ii) 4p² - 25q²

       Ans:

       i) 169m² - 625n² = (13m)² - (25n)²

                                   = (13m + 25n)(13m - 25n)

       ii) 4p² - 25q²       = (2p)² - (5q)²                       [a² - b² = (a + b)(a - b)]

                                   = (2p + 5q) (2p - 5q)

32.Factorise

   i) x² +7x + 12               ii) p² - 6p + 8

       Ans:

       i) x² +7x + 12         = x² + 3x + 4x +12

                                     = x( x+ 3) + 4(x + 3)

                                     = (x + 3) (x + 4)

       ii) p² - 6p + 8         = p² - 4p - 2p + 8

                                     = p(p - 4) -2(p - 4)

                                     = (p - 4) (p -2)

33.Simplify

   (i) 16x⁴ ÷ 32x                   (ii) ^-4 2y³ ÷ 7y²

       Ans:

34.Simplify

   i) (5y³ - 4y² + 3y) ÷ y               ii) (9x⁵ - 15x⁴ - 21x²) ÷ 3x²

       Ans:

35.Simplify

   i) (x² + 7x + 10) ÷ (x + 2)               ii) (a² + 24a + 144) ÷ (a + 12)

       Ans:

36.Solve 3x + 5 = 23.

       Ans:

       3x + 5 = 23 → 3x = 32 - 5 (transposing 5 to R.H.S)

                                   = 18

                           x = 18/3 = 6.

37.Solve 17 = 10 - y.

       Ans:

       17 = 10 - y → 17 - 10 = ^-y (transposing 10 to L H S)

                         →  7 = ^-y  → y = 7.

38.Solve 3(3x - 7) = 5(2x - 3).

      Ans:

      3(3x - 7) = 5(2x - 3) → 9x - 21 = 10x - 15

                                      → 9x - 10x = ^-15 + 21

                                      → ^-x = 6 → x = 6.

39.

       Ans:

40.

       Ans:

       L CM of 3, 4 and 2 is 12

       multiplying throughout by 12,

        → 4m + 3m = 6  → 7m = 6  →