Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 940 · 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 52² − 37².
2. 2.Use (a + b)² = a² + 2ab + b² to find 36².
3. 3.Find the value of x² + 2xy + y² when x = 8 and y = 1.
4. 4.Use (a − b)² = a² − 2ab + b² to find 25².
5. 5.Use (a + b)(a − b) = a² − b² to find 32 × 28.
6. 6.Use (a − b)² = a² − 2ab + b² to find 58².
7. 7.Use (a + b)² = a² + 2ab + b² to find 16².
8. 8.Use (a + b)² = a² + 2ab + b² to find 48².
9. 9.Use (a − b)² = a² − 2ab + b² to find 32².
10. 10.Use (a + b)² = a² + 2ab + b² to find 59².
11. 11.Find the value of x² − 2xy + y² when x = 8 and y = 1.
12. 12.Use (a − b)² = a² − 2ab + b² to find 72².
13. 13.Use (a + b)² = a² + 2ab + b² to find 24².
14. 14.Use (a − b)² = a² − 2ab + b² to find 51².
15. 15.Use (a − b)² = a² − 2ab + b² to find 69².
16. 16.Use (a − b)² = a² − 2ab + b² to find 31².
17. 17.Use (a + b)(a − b) = a² − b² to find 21 × 19.
18. 18.Find the value of x² + 2xy + y² when x = 14 and y = 10.
19. 19.Find the value of x² − 2xy + y² when x = 5 and y = 2.
20. 20.Use a² − b² = (a + b)(a − b) to find 64² − 61².
21. 21.Use (a + b)² = a² + 2ab + b² to find 28².
22. 22.Use a² − b² = (a + b)(a − b) to find 82² − 23².
23. 23.Use a² − b² = (a + b)(a − b) to find 86² − 27².
24. 24.Use a² − b² = (a + b)(a − b) to find 80² − 35².
25. 25.If a + b = 13 and ab = 30, what is a² + b²?
26. 26.Use (a + b)² = a² + 2ab + b² to find 88².
27. 27.Find the value of x² − y² when x = 8 and y = 3.
28. 28.Find the value of x² − y² when x = 13 and y = 7.
29. 29.Use (a − b)² = a² − 2ab + b² to find 88².
30. 30.Use (a − b)² = a² − 2ab + b² to find 59².
31. 31.Use (a + b)² = a² + 2ab + b² to find 57².
32. 32.Use (a − b)² = a² − 2ab + b² to find 61².
33. 33.Use (a + b)² = a² + 2ab + b² to find 69².
34. 34.Use (a − b)² = a² − 2ab + b² to find 75².
35. 35.Use a² − b² = (a + b)(a − b) to find 66² − 31².
36. 36.Use a² − b² = (a + b)(a − b) to find 64² − 38².
37. 37.Use (a − b)² = a² − 2ab + b² to find 18².
38. 38.Use (a − b)² = a² − 2ab + b² to find 52².
39. 39.Find the value of x² − 2xy + y² when x = 13 and y = 9.
40. 40.If a + b = 9 and ab = 20, what is a² + b²?

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