Class 6 Maths Worksheet on Algebra Word Problems

I'll solve each problem step by step, checking my calculations carefully.

Given values: p = -2, q = -1, r = 3

Problem 1: p² + q² - r²
- p² = (-2)² = 4
- q² = (-1)² = 1
- r² = 3² = 9
- p² + q² - r² = 4 + 1 - 9 = 5 - 9 = -4

Problem 2: 2p² - q² + 3r²
- 2p² = 2 × (-2)² = 2 × 4 = 8
- q² = (-1)² = 1
- 3r² = 3 × 3² = 3 × 9 = 27
- 2p² - q² + 3r² = 8 - 1 + 27 = 7 + 27 = 34

Problem 3: p - q - r
- p - q - r = -2 - (-1) - 3 = -2 + 1 - 3 = -1 - 3 = -4

Problem 4: p⁴ + q⁴ - r⁴
- p⁴ = (-2) = 16
- q⁴ = (-1)⁴ = 1
- r = 3⁴ = 81
- p⁴ + q⁴ - r = 16 + 1 - 81 = 17 - 81 = -64

Problem 5: p³ + q³ + r³ + 3pqr
- p³ = (-2)³ = -8
- q³ = (-1)³ = -1
- r³ = 3³ = 27
- 3pqr = 3 × (-2) × (-1) × 3 = 3 × 6 = 18
- p³ + q³ + r³ + 3pqr = -8 + (-1) + 27 + 18 = -9 + 27 + 18 = 18 + 18 = 36

Problem 6: Perimeter of equilateral triangle with side l
An equilateral triangle has 3 equal sides, so perimeter = 3l

Problem 7: Perimeter of regular hexagon with side l
A regular hexagon has 6 equal sides, so perimeter = 6l

Problem 8: Total length of edges of a cube with edge length l
A cube has 12 edges (each face has 4 edges, but edges are shared). So total length = 12l

Problem 9: Constant term of 3x² + 5x + 8
The constant term is the number without any variable: 8

Problem 10: Constant term of 2x² - 9
The constant term is: -9

Final Answer:
1. -4
2. 34
3. -4
4. -64
5. 36
6. 3l
7. 6l
8. 12l
9. 8
10. -9