Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 502 · 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 67².
2. 2.Use a² − b² = (a + b)(a − b) to find 25² − 4².
3. 3.If a − b = 1 and ab = 6, what is a² + b²?
4. 4.Use (a + b)² = a² + 2ab + b² to find 24².
5. 5.If a + b = 17 and ab = 70, what is a² + b²?
6. 6.Use a² − b² = (a + b)(a − b) to find 56² − 41².
7. 7.Use a² − b² = (a + b)(a − b) to find 92² − 23².
8. 8.If a − b = 6 and ab = 72, what is a² + b²?
9. 9.Use (a − b)² = a² − 2ab + b² to find 92².
10. 10.Use (a + b)(a − b) = a² − b² to find 96 × 84.
11. 11.If a + b = 4 and ab = 3, what is a² + b²?
12. 12.Use (a − b)² = a² − 2ab + b² to find 85².
13. 13.Use (a + b)(a − b) = a² − b² to find 43 × 37.
14. 14.Use (a + b)² = a² + 2ab + b² to find 46².
15. 15.Find the value of x² − y² when x = 13 and y = 1.
16. 16.Use a² − b² = (a + b)(a − b) to find 96² − 19².
17. 17.Use (a + b)(a − b) = a² − b² to find 68 × 52.
18. 18.If a + b = 22 and ab = 120, what is a² + b²?
19. 19.Use (a + b)² = a² + 2ab + b² to find 65².
20. 20.Use (a + b)(a − b) = a² − b² to find 29 × 11.
21. 21.Find the value of x² + 2xy + y² when x = 7 and y = 6.
22. 22.Use a² − b² = (a + b)(a − b) to find 49² − 9².
23. 23.If a + b = 12 and ab = 32, what is a² + b²?
24. 24.If a − b = 2 and ab = 99, what is a² + b²?
25. 25.Use (a − b)² = a² − 2ab + b² to find 28².
26. 26.If a + b = 7 and ab = 10, what is a² + b²?
27. 27.Use (a + b)(a − b) = a² − b² to find 47 × 33.
28. 28.If a − b = 2 and ab = 120, what is a² + b²?
29. 29.Use a² − b² = (a + b)(a − b) to find 50² − 27².
30. 30.If a − b = 6 and ab = 16, what is a² + b²?
31. 31.If a + b = 11 and ab = 30, what is a² + b²?
32. 32.Use a² − b² = (a + b)(a − b) to find 20² − 15².
33. 33.Use (a + b)² = a² + 2ab + b² to find 91².
34. 34.Use (a + b)² = a² + 2ab + b² to find 86².
35. 35.Use (a − b)² = a² − 2ab + b² to find 66².
36. 36.Use (a + b)(a − b) = a² − b² to find 23 × 17.
37. 37.Find the value of x² + 2xy + y² when x = 7 and y = 5.
38. 38.Use (a + b)(a − b) = a² − b² to find 46 × 34.
39. 39.If a + b = 10 and ab = 21, what is a² + b²?
40. 40.Use (a + b)² = a² + 2ab + b² to find 55².

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