Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 398 · 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 a² − b² = (a + b)(a − b) to find 64² − 13².
2. 2.Use (a + b)² = a² + 2ab + b² to find 69².
3. 3.Use (a + b)² = a² + 2ab + b² to find 33².
4. 4.Use (a + b)(a − b) = a² − b² to find 92 × 88.
5. 5.Use (a + b)² = a² + 2ab + b² to find 13².
6. 6.Use (a − b)² = a² − 2ab + b² to find 83².
7. 7.Use (a + b)² = a² + 2ab + b² to find 37².
8. 8.Find the value of x² + 2xy + y² when x = 8 and y = 7.
9. 9.Use (a + b)(a − b) = a² − b² to find 67 × 53.
10. 10.Use a² − b² = (a + b)(a − b) to find 90² − 65².
11. 11.Find the value of x² − y² when x = 11 and y = 10.
12. 12.Use (a + b)(a − b) = a² − b² to find 74 × 66.
13. 13.Use (a + b)(a − b) = a² − b² to find 69 × 51.
14. 14.Use (a − b)² = a² − 2ab + b² to find 15².
15. 15.Use (a − b)² = a² − 2ab + b² to find 98².
16. 16.If a + b = 18 and ab = 77, what is a² + b²?
17. 17.Use (a + b)² = a² + 2ab + b² to find 88².
18. 18.Use (a + b)(a − b) = a² − b² to find 58 × 42.
19. 19.If a + b = 10 and ab = 16, what is a² + b²?
20. 20.Use a² − b² = (a + b)(a − b) to find 60² − 17².
21. 21.Use (a − b)² = a² − 2ab + b² to find 68².
22. 22.Use a² − b² = (a + b)(a − b) to find 28² − 19².
23. 23.Use a² − b² = (a + b)(a − b) to find 42² − 30².
24. 24.Use (a + b)² = a² + 2ab + b² to find 87².
25. 25.If a − b = 2 and ab = 3, what is a² + b²?
26. 26.Use a² − b² = (a + b)(a − b) to find 54² − 49².
27. 27.Use (a + b)² = a² + 2ab + b² to find 41².
28. 28.If a − b = 8 and ab = 48, what is a² + b²?
29. 29.Use (a + b)² = a² + 2ab + b² to find 106².
30. 30.Use (a + b)(a − b) = a² − b² to find 61 × 59.
31. 31.Use (a − b)² = a² − 2ab + b² to find 45².
32. 32.Use a² − b² = (a + b)(a − b) to find 94² − 82².
33. 33.If a − b = 4 and ab = 5, what is a² + b²?
34. 34.Use (a + b)² = a² + 2ab + b² to find 12².
35. 35.Use a² − b² = (a + b)(a − b) to find 88² − 55².
36. 36.Use (a − b)² = a² − 2ab + b² to find 53².
37. 37.Use (a + b)(a − b) = a² − b² to find 29 × 11.
38. 38.If a + b = 9 and ab = 14, what is a² + b²?
39. 39.If a − b = 2 and ab = 35, what is a² + b²?
40. 40.Use (a + b)² = a² + 2ab + b² to find 14².

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