Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 705 · 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 65².
2. 2.If a + b = 23 and ab = 132, what is a² + b²?
3. 3.Find the value of x² − y² when x = 6 and y = 1.
4. 4.Use (a + b)² = a² + 2ab + b² to find 59².
5. 5.Use (a + b)(a − b) = a² − b² to find 101 × 99.
6. 6.Use (a − b)² = a² − 2ab + b² to find 17².
7. 7.If a − b = 1 and ab = 6, what is a² + b²?
8. 8.Use (a + b)(a − b) = a² − b² to find 46 × 34.
9. 9.Use (a + b)² = a² + 2ab + b² to find 45².
10. 10.Use (a + b)² = a² + 2ab + b² to find 86².
11. 11.Use a² − b² = (a + b)(a − b) to find 91² − 15².
12. 12.If a − b = 1 and ab = 30, what is a² + b²?
13. 13.Use a² − b² = (a + b)(a − b) to find 66² − 40².
14. 14.Use (a − b)² = a² − 2ab + b² to find 68².
15. 15.Find the value of x² + 2xy + y² when x = 6 and y = 2.
16. 16.Use (a + b)(a − b) = a² − b² to find 75 × 65.
17. 17.Use (a + b)² = a² + 2ab + b² to find 15².
18. 18.Use (a + b)² = a² + 2ab + b² to find 29².
19. 19.Find the value of x² + 2xy + y² when x = 4 and y = 1.
20. 20.Use (a − b)² = a² − 2ab + b² to find 26².
21. 21.Use a² − b² = (a + b)(a − b) to find 98² − 13².
22. 22.If a + b = 12 and ab = 27, what is a² + b²?
23. 23.Use (a + b)(a − b) = a² − b² to find 84 × 76.
24. 24.Use (a − b)² = a² − 2ab + b² to find 58².
25. 25.Find the value of x² − 2xy + y² when x = 7 and y = 3.
26. 26.Use (a + b)² = a² + 2ab + b² to find 94².
27. 27.Use a² − b² = (a + b)(a − b) to find 31² − 16².
28. 28.Use (a − b)² = a² − 2ab + b² to find 56².
29. 29.Find the value of x² + 2xy + y² when x = 15 and y = 1.
30. 30.Use a² − b² = (a + b)(a − b) to find 51² − 22².
31. 31.Use (a − b)² = a² − 2ab + b² to find 65².
32. 32.Use a² − b² = (a + b)(a − b) to find 21² − 15².
33. 33.Use (a − b)² = a² − 2ab + b² to find 31².
34. 34.Use (a − b)² = a² − 2ab + b² to find 52².
35. 35.Find the value of x² + 2xy + y² when x = 13 and y = 4.
36. 36.If a − b = 2 and ab = 3, what is a² + b²?
37. 37.If a + b = 5 and ab = 6, what is a² + b²?
38. 38.Use (a + b)(a − b) = a² − b² to find 102 × 98.
39. 39.If a − b = 4 and ab = 5, what is a² + b²?
40. 40.Use (a + b)² = a² + 2ab + b² to find 68².

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