Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 392 · 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 88².
2. 2.Use (a + b)² = a² + 2ab + b² to find 72².
3. 3.Find the value of x² − 2xy + y² when x = 7 and y = 1.
4. 4.Use (a − b)² = a² − 2ab + b² to find 37².
5. 5.Use (a + b)² = a² + 2ab + b² to find 61².
6. 6.Use (a + b)² = a² + 2ab + b² to find 16².
7. 7.Use (a + b)² = a² + 2ab + b² to find 22².
8. 8.If a − b = 1 and ab = 132, what is a² + b²?
9. 9.If a + b = 9 and ab = 20, what is a² + b²?
10. 10.Use (a − b)² = a² − 2ab + b² to find 19².
11. 11.Find the value of x² + 2xy + y² when x = 5 and y = 4.
12. 12.Use a² − b² = (a + b)(a − b) to find 20² − 12².
13. 13.If a + b = 15 and ab = 44, what is a² + b²?
14. 14.Use (a + b)(a − b) = a² − b² to find 67 × 53.
15. 15.Use (a − b)² = a² − 2ab + b² to find 31².
16. 16.Use (a + b)² = a² + 2ab + b² to find 102².
17. 17.Use (a + b)² = a² + 2ab + b² to find 12².
18. 18.Find the value of x² − 2xy + y² when x = 15 and y = 5.
19. 19.Use a² − b² = (a + b)(a − b) to find 64² − 33².
20. 20.If a − b = 3 and ab = 4, what is a² + b²?
21. 21.Use a² − b² = (a + b)(a − b) to find 37² − 34².
22. 22.Use a² − b² = (a + b)(a − b) to find 53² − 9².
23. 23.Use (a + b)(a − b) = a² − b² to find 75 × 65.
24. 24.Use (a + b)² = a² + 2ab + b² to find 105².
25. 25.Use (a − b)² = a² − 2ab + b² to find 44².
26. 26.Use (a + b)(a − b) = a² − b² to find 105 × 95.
27. 27.Use (a − b)² = a² − 2ab + b² to find 45².
28. 28.Use a² − b² = (a + b)(a − b) to find 32² − 8².
29. 29.Use a² − b² = (a + b)(a − b) to find 84² − 65².
30. 30.If a + b = 15 and ab = 50, what is a² + b²?
31. 31.Use (a + b)² = a² + 2ab + b² to find 107².
32. 32.Use (a − b)² = a² − 2ab + b² to find 36².
33. 33.If a − b = 1 and ab = 2, what is a² + b²?
34. 34.Use (a − b)² = a² − 2ab + b² to find 83².
35. 35.Use (a + b)(a − b) = a² − b² to find 77 × 63.
36. 36.Use (a − b)² = a² − 2ab + b² to find 73².
37. 37.Find the value of x² + 2xy + y² when x = 7 and y = 6.
38. 38.Use (a + b)(a − b) = a² − b² to find 42 × 38.
39. 39.Use (a − b)² = a² − 2ab + b² to find 29².
40. 40.Use (a + b)² = a² + 2ab + b² to find 76².

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