Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 618 · 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)(a − b) = a² − b² to find 31 × 29.
2. 2.Use a² − b² = (a + b)(a − b) to find 59² − 46².
3. 3.Use (a − b)² = a² − 2ab + b² to find 28².
4. 4.Use (a − b)² = a² − 2ab + b² to find 69².
5. 5.Use (a + b)(a − b) = a² − b² to find 72 × 68.
6. 6.Use (a + b)² = a² + 2ab + b² to find 23².
7. 7.Use a² − b² = (a + b)(a − b) to find 96² − 69².
8. 8.Use (a − b)² = a² − 2ab + b² to find 24².
9. 9.If a + b = 10 and ab = 21, what is a² + b²?
10. 10.Use (a − b)² = a² − 2ab + b² to find 84².
11. 11.Use (a + b)(a − b) = a² − b² to find 52 × 48.
12. 12.Use (a + b)(a − b) = a² − b² to find 75 × 65.
13. 13.If a − b = 2 and ab = 3, what is a² + b²?
14. 14.If a − b = 8 and ab = 33, what is a² + b²?
15. 15.Use (a + b)(a − b) = a² − b² to find 56 × 44.
16. 16.Use (a − b)² = a² − 2ab + b² to find 63².
17. 17.Use (a + b)² = a² + 2ab + b² to find 86².
18. 18.Use (a + b)² = a² + 2ab + b² to find 21².
19. 19.Use (a + b)(a − b) = a² − b² to find 29 × 11.
20. 20.Find the value of x² + 2xy + y² when x = 5 and y = 4.
21. 21.Use a² − b² = (a + b)(a − b) to find 70² − 61².
22. 22.Use a² − b² = (a + b)(a − b) to find 33² − 12².
23. 23.Use a² − b² = (a + b)(a − b) to find 36² − 32².
24. 24.If a + b = 3 and ab = 2, what is a² + b²?
25. 25.Use (a − b)² = a² − 2ab + b² to find 72².
26. 26.Use a² − b² = (a + b)(a − b) to find 56² − 49².
27. 27.Use (a − b)² = a² − 2ab + b² to find 71².
28. 28.If a − b = 1 and ab = 20, what is a² + b²?
29. 29.If a + b = 12 and ab = 35, what is a² + b²?
30. 30.Use (a + b)² = a² + 2ab + b² to find 98².
31. 31.Use (a + b)² = a² + 2ab + b² to find 36².
32. 32.If a − b = 3 and ab = 10, what is a² + b²?
33. 33.If a + b = 7 and ab = 12, what is a² + b²?
34. 34.If a − b = 9 and ab = 22, what is a² + b²?
35. 35.If a − b = 1 and ab = 12, what is a² + b²?
36. 36.Use (a + b)(a − b) = a² − b² to find 24 × 16.
37. 37.Use a² − b² = (a + b)(a − b) to find 76² − 61².
38. 38.Use (a + b)(a − b) = a² − b² to find 64 × 56.
39. 39.Find the value of x² − y² when x = 3 and y = 1.
40. 40.Use (a + b)² = a² + 2ab + b² to find 83².

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