Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 757 · 40 sums

The method (Split into easy parts): (a + b)² = a² + 2ab + b². (a − b)² = a² − 2ab + b². (a + b)(a − b) = a² − b²; so a² − b² = (a + b)(a − b). a² + b² = (a + b)² − 2ab = (a − b)² + 2ab.

1. 1.If a − b = 2 and ab = 24, what is a² + b²?
2. 2.If a + b = 9 and ab = 14, what is a² + b²?
3. 3.Find the value of x² + 2xy + y² when x = 15 and y = 2.
4. 4.Use (a + b)² = a² + 2ab + b² to find 105².
5. 5.Use (a − b)² = a² − 2ab + b² to find 49².
6. 6.If a + b = 7 and ab = 12, what is a² + b²?
7. 7.If a + b = 6 and ab = 8, what is a² + b²?
8. 8.Use (a + b)² = a² + 2ab + b² to find 94².
9. 9.Find the value of x² − y² when x = 14 and y = 6.
10. 10.Use a² − b² = (a + b)(a − b) to find 33² − 27².
11. 11.Find the value of x² − y² when x = 8 and y = 1.
12. 12.If a − b = 1 and ab = 56, what is a² + b²?
13. 13.If a − b = 6 and ab = 16, what is a² + b²?
14. 14.If a + b = 14 and ab = 24, what is a² + b²?
15. 15.Use (a − b)² = a² − 2ab + b² to find 16².
16. 16.Use (a + b)² = a² + 2ab + b² to find 54².
17. 17.Use a² − b² = (a + b)(a − b) to find 82² − 10².
18. 18.Use (a + b)(a − b) = a² − b² to find 93 × 87.
19. 19.Use (a + b)(a − b) = a² − b² to find 82 × 78.
20. 20.Use (a + b)(a − b) = a² − b² to find 35 × 25.
21. 21.Use a² − b² = (a + b)(a − b) to find 31² − 2².
22. 22.If a + b = 8 and ab = 12, what is a² + b²?
23. 23.Use (a + b)(a − b) = a² − b² to find 44 × 36.
24. 24.Find the value of x² + 2xy + y² when x = 4 and y = 3.
25. 25.Use (a + b)² = a² + 2ab + b² to find 85².
26. 26.Use (a + b)(a − b) = a² − b² to find 38 × 22.
27. 27.Find the value of x² + 2xy + y² when x = 7 and y = 4.
28. 28.Use a² − b² = (a + b)(a − b) to find 40² − 11².
29. 29.Find the value of x² − 2xy + y² when x = 4 and y = 2.
30. 30.Use (a + b)² = a² + 2ab + b² to find 11².
31. 31.Use (a + b)² = a² + 2ab + b² to find 98².
32. 32.Use (a + b)(a − b) = a² − b² to find 88 × 72.
33. 33.Use (a + b)(a − b) = a² − b² to find 31 × 29.
34. 34.Use (a − b)² = a² − 2ab + b² to find 17².
35. 35.Find the value of x² − 2xy + y² when x = 11 and y = 5.
36. 36.Use (a + b)² = a² + 2ab + b² to find 107².
37. 37.Use a² − b² = (a + b)(a − b) to find 75² − 10².
38. 38.Use a² − b² = (a + b)(a − b) to find 60² − 4².
39. 39.Use (a − b)² = a² − 2ab + b² to find 29².
40. 40.If a + b = 9 and ab = 8, what is a² + b²?

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