Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 597 · 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.Use (a + b)² = a² + 2ab + b² to find 24².
2. 2.Use (a − b)² = a² − 2ab + b² to find 15².
3. 3.Use (a + b)(a − b) = a² − b² to find 21 × 19.
4. 4.Find the value of x² − 2xy + y² when x = 8 and y = 7.
5. 5.Use (a + b)² = a² + 2ab + b² to find 67².
6. 6.Use a² − b² = (a + b)(a − b) to find 22² − 8².
7. 7.Use (a + b)² = a² + 2ab + b² to find 76².
8. 8.Use (a + b)(a − b) = a² − b² to find 105 × 95.
9. 9.If a + b = 18 and ab = 80, what is a² + b²?
10. 10.Use a² − b² = (a + b)(a − b) to find 82² − 62².
11. 11.Use (a − b)² = a² − 2ab + b² to find 12².
12. 12.Use (a + b)² = a² + 2ab + b² to find 74².
13. 13.Use a² − b² = (a + b)(a − b) to find 69² − 26².
14. 14.If a + b = 21 and ab = 108, what is a² + b²?
15. 15.Use (a − b)² = a² − 2ab + b² to find 11².
16. 16.Use (a + b)² = a² + 2ab + b² to find 106².
17. 17.Use (a + b)² = a² + 2ab + b² to find 11².
18. 18.Use (a + b)² = a² + 2ab + b² to find 12².
19. 19.Use a² − b² = (a + b)(a − b) to find 94² − 93².
20. 20.Use (a − b)² = a² − 2ab + b² to find 32².
21. 21.Use a² − b² = (a + b)(a − b) to find 81² − 14².
22. 22.Use (a + b)² = a² + 2ab + b² to find 31².
23. 23.Use (a − b)² = a² − 2ab + b² to find 14².
24. 24.Use (a + b)² = a² + 2ab + b² to find 72².
25. 25.Use (a − b)² = a² − 2ab + b² to find 82².
26. 26.Use (a + b)(a − b) = a² − b² to find 95 × 85.
27. 27.Use (a − b)² = a² − 2ab + b² to find 36².
28. 28.Use (a + b)(a − b) = a² − b² to find 42 × 38.
29. 29.If a − b = 6 and ab = 55, what is a² + b²?
30. 30.Find the value of x² − 2xy + y² when x = 13 and y = 11.
31. 31.Use a² − b² = (a + b)(a − b) to find 31² − 21².
32. 32.If a + b = 14 and ab = 40, what is a² + b²?
33. 33.Use (a + b)(a − b) = a² − b² to find 35 × 25.
34. 34.Use (a − b)² = a² − 2ab + b² to find 89².
35. 35.Use (a − b)² = a² − 2ab + b² to find 31².
36. 36.If a + b = 3 and ab = 2, what is a² + b²?
37. 37.Use (a + b)² = a² + 2ab + b² to find 73².
38. 38.Use (a − b)² = a² − 2ab + b² to find 79².
39. 39.Use a² − b² = (a + b)(a − b) to find 20² − 15².
40. 40.Use a² − b² = (a + b)(a − b) to find 26² − 12².

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