Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 989 · 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 61².
2. 2.Use (a + b)² = a² + 2ab + b² to find 61².
3. 3.If a + b = 7 and ab = 12, what is a² + b²?
4. 4.Use (a + b)² = a² + 2ab + b² to find 77².
5. 5.Use (a + b)(a − b) = a² − b² to find 79 × 61.
6. 6.Use (a − b)² = a² − 2ab + b² to find 93².
7. 7.Use (a − b)² = a² − 2ab + b² to find 32².
8. 8.If a + b = 18 and ab = 77, what is a² + b²?
9. 9.If a + b = 15 and ab = 44, what is a² + b²?
10. 10.Use (a + b)(a − b) = a² − b² to find 61 × 59.
11. 11.If a + b = 5 and ab = 6, what is a² + b²?
12. 12.Find the value of x² + 2xy + y² when x = 15 and y = 9.
13. 13.Use (a − b)² = a² − 2ab + b² to find 29².
14. 14.Use (a + b)² = a² + 2ab + b² to find 67².
15. 15.Use (a + b)(a − b) = a² − b² to find 62 × 58.
16. 16.Use (a + b)² = a² + 2ab + b² to find 27².
17. 17.Find the value of x² − y² when x = 8 and y = 1.
18. 18.Use (a + b)² = a² + 2ab + b² to find 35².
19. 19.Use (a + b)(a − b) = a² − b² to find 93 × 87.
20. 20.If a − b = 8 and ab = 20, what is a² + b²?
21. 21.Use (a − b)² = a² − 2ab + b² to find 66².
22. 22.Find the value of x² − 2xy + y² when x = 15 and y = 6.
23. 23.Use a² − b² = (a + b)(a − b) to find 52² − 22².
24. 24.Find the value of x² − y² when x = 3 and y = 1.
25. 25.If a − b = 1 and ab = 2, what is a² + b²?
26. 26.If a + b = 6 and ab = 5, what is a² + b²?
27. 27.Find the value of x² + 2xy + y² when x = 14 and y = 1.
28. 28.Find the value of x² + 2xy + y² when x = 8 and y = 5.
29. 29.Use (a + b)² = a² + 2ab + b² to find 11².
30. 30.Use (a + b)² = a² + 2ab + b² to find 72².
31. 31.If a + b = 3 and ab = 2, what is a² + b²?
32. 32.If a − b = 1 and ab = 12, what is a² + b²?
33. 33.Find the value of x² + 2xy + y² when x = 3 and y = 2.
34. 34.Find the value of x² + 2xy + y² when x = 8 and y = 1.
35. 35.Find the value of x² − y² when x = 10 and y = 6.
36. 36.Use (a − b)² = a² − 2ab + b² to find 16².
37. 37.Use (a + b)² = a² + 2ab + b² to find 13².
38. 38.Use a² − b² = (a + b)(a − b) to find 77² − 65².
39. 39.Use (a + b)² = a² + 2ab + b² to find 71².
40. 40.Use a² − b² = (a + b)(a − b) to find 61² − 52².

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