2.4. Solved problems

1. Evaluate: x² + 2xy + y² for x = -1, y = 2

   (-1)2 + 2(-1)2 + 22 = 1 - 4 + 4 = 1
   

2. Evaluate: (x² + y² + z²)^1/2 for x = 2, y = -1, z = 3

   [22 + (-1)2 + 32]1/2 = 
   (4 + 1 + 9)1/2 = √14
   

3. Evaluate: x·sin 30° + y·cos 30° for x = 2, y = 3

   2×0.5 + 3×0.866 = 1 + 2.598 = 3.598
   

4. Evaluate: 3 + |x - y| for x = -2, y = 4

   3 + |-2 - 4| = 3 + |-6| = 3 + 6 = 9
   

5. Evaluate: x² + 2x - y² + 4y for x = -2, y = -2

   (-2)2 + 2(-2) - (-2)2 + 4(-2) = 4 - 4 - 4 - 8 = -12
   

6. Evaluate: x·cos 30° - y·sin 30° for x = 2, y = 3

   2×0.866 - 3×0.5 = 1.732 - 1.5 = 0.232
   

7. Evaluate: x{x[x(16x + 8) + 4] + 2} + 1 for x = 2

   2×{2×[2×(16×2 + 8) + 4] + 2} + 1 =
   2×{×2×[80 + 4] + 2} + 1 =
   2×{168 + 2} + 1 =
   340 + 1 = 341
   

   How many multiplications? 4

8. Evaluate: 16x⁴ + 8x³ + 4x² + 2x + 1 for x = 2

   16(2)4 + 8(2)3 + 4(2)2 + 2(2) + 1 =
   16×16 + 8×8 + 4×4 + 2×2 + 1 = 
   256 + 64 + 16 + 4 + 1 = 341
   

   How many multiplications? 10