Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 231 · 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.Find the value of x² − y² when x = 14 and y = 7.
2. 2.Use a² − b² = (a + b)(a − b) to find 83² − 55².
3. 3.Use (a + b)² = a² + 2ab + b² to find 23².
4. 4.Find the value of x² − 2xy + y² when x = 13 and y = 2.
5. 5.If a − b = 3 and ab = 54, what is a² + b²?
6. 6.Find the value of x² + 2xy + y² when x = 11 and y = 6.
7. 7.Use (a − b)² = a² − 2ab + b² to find 61².
8. 8.Use (a − b)² = a² − 2ab + b² to find 33².
9. 9.Use (a − b)² = a² − 2ab + b² to find 35².
10. 10.If a + b = 10 and ab = 24, what is a² + b²?
11. 11.Find the value of x² + 2xy + y² when x = 15 and y = 3.
12. 12.Use (a − b)² = a² − 2ab + b² to find 36².
13. 13.Use (a + b)(a − b) = a² − b² to find 31 × 29.
14. 14.Use (a + b)(a − b) = a² − b² to find 107 × 93.
15. 15.Find the value of x² + 2xy + y² when x = 4 and y = 1.
16. 16.Use (a − b)² = a² − 2ab + b² to find 71².
17. 17.Use (a − b)² = a² − 2ab + b² to find 87².
18. 18.If a + b = 7 and ab = 6, what is a² + b²?
19. 19.If a + b = 3 and ab = 2, what is a² + b²?
20. 20.If a − b = 2 and ab = 80, what is a² + b²?
21. 21.Use (a + b)(a − b) = a² − b² to find 87 × 73.
22. 22.Use (a + b)² = a² + 2ab + b² to find 102².
23. 23.Use (a + b)(a − b) = a² − b² to find 83 × 77.
24. 24.Use (a − b)² = a² − 2ab + b² to find 68².
25. 25.Use (a − b)² = a² − 2ab + b² to find 31².
26. 26.Use (a − b)² = a² − 2ab + b² to find 69².
27. 27.Use (a + b)² = a² + 2ab + b² to find 101².
28. 28.Find the value of x² − y² when x = 14 and y = 13.
29. 29.Use a² − b² = (a + b)(a − b) to find 60² − 27².
30. 30.Use (a − b)² = a² − 2ab + b² to find 67².
31. 31.Use (a − b)² = a² − 2ab + b² to find 46².
32. 32.If a − b = 4 and ab = 12, what is a² + b²?
33. 33.Use (a + b)² = a² + 2ab + b² to find 82².
34. 34.If a + b = 5 and ab = 4, what is a² + b²?
35. 35.Find the value of x² − y² when x = 14 and y = 4.
36. 36.Use (a + b)² = a² + 2ab + b² to find 13².
37. 37.Find the value of x² + 2xy + y² when x = 7 and y = 1.
38. 38.If a + b = 4 and ab = 3, what is a² + b²?
39. 39.Use a² − b² = (a + b)(a − b) to find 69² − 51².
40. 40.Use (a + b)² = a² + 2ab + b² to find 104².

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