Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 991 · 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 27².
2. 2.Use (a + b)² = a² + 2ab + b² to find 23².
3. 3.Use a² − b² = (a + b)(a − b) to find 42² − 41².
4. 4.Find the value of x² − y² when x = 13 and y = 4.
5. 5.Find the value of x² − 2xy + y² when x = 8 and y = 6.
6. 6.Find the value of x² − 2xy + y² when x = 9 and y = 1.
7. 7.If a − b = 2 and ab = 3, what is a² + b²?
8. 8.If a − b = 2 and ab = 8, what is a² + b²?
9. 9.Find the value of x² + 2xy + y² when x = 6 and y = 5.
10. 10.If a + b = 6 and ab = 5, what is a² + b²?
11. 11.Use (a − b)² = a² − 2ab + b² to find 37².
12. 12.Use a² − b² = (a + b)(a − b) to find 43² − 32².
13. 13.If a − b = 4 and ab = 12, what is a² + b²?
14. 14.Use (a − b)² = a² − 2ab + b² to find 89².
15. 15.Use (a − b)² = a² − 2ab + b² to find 12².
16. 16.Find the value of x² − y² when x = 12 and y = 1.
17. 17.Use (a + b)² = a² + 2ab + b² to find 97².
18. 18.Use (a + b)(a − b) = a² − b² to find 83 × 77.
19. 19.Use (a + b)² = a² + 2ab + b² to find 103².
20. 20.Use (a + b)² = a² + 2ab + b² to find 25².
21. 21.Use a² − b² = (a + b)(a − b) to find 22² − 21².
22. 22.Use (a + b)² = a² + 2ab + b² to find 26².
23. 23.Use a² − b² = (a + b)(a − b) to find 74² − 35².
24. 24.Use (a + b)(a − b) = a² − b² to find 43 × 37.
25. 25.If a − b = 1 and ab = 2, what is a² + b²?
26. 26.Use a² − b² = (a + b)(a − b) to find 38² − 23².
27. 27.Use (a − b)² = a² − 2ab + b² to find 75².
28. 28.Use (a + b)² = a² + 2ab + b² to find 71².
29. 29.Find the value of x² − y² when x = 4 and y = 2.
30. 30.Find the value of x² − 2xy + y² when x = 11 and y = 2.
31. 31.Use a² − b² = (a + b)(a − b) to find 70² − 59².
32. 32.Find the value of x² − 2xy + y² when x = 5 and y = 1.
33. 33.Use (a + b)² = a² + 2ab + b² to find 17².
34. 34.Use (a + b)² = a² + 2ab + b² to find 35².
35. 35.Use (a + b)² = a² + 2ab + b² to find 21².
36. 36.Find the value of x² − 2xy + y² when x = 6 and y = 1.
37. 37.Use a² − b² = (a + b)(a − b) to find 69² − 57².
38. 38.Use (a + b)(a − b) = a² − b² to find 79 × 61.
39. 39.Use (a + b)(a − b) = a² − b² to find 66 × 54.
40. 40.If a − b = 5 and ab = 14, what is a² + b²?

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