Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 571 · 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 96².
2. 2.If a − b = 9 and ab = 22, what is a² + b²?
3. 3.If a − b = 3 and ab = 4, what is a² + b²?
4. 4.Use (a − b)² = a² − 2ab + b² to find 59².
5. 5.Use (a + b)(a − b) = a² − b² to find 68 × 52.
6. 6.Use (a + b)² = a² + 2ab + b² to find 22².
7. 7.Use (a + b)² = a² + 2ab + b² to find 65².
8. 8.If a + b = 11 and ab = 18, what is a² + b²?
9. 9.Use (a + b)(a − b) = a² − b² to find 66 × 54.
10. 10.Use (a + b)² = a² + 2ab + b² to find 81².
11. 11.Use (a − b)² = a² − 2ab + b² to find 52².
12. 12.Use (a − b)² = a² − 2ab + b² to find 67².
13. 13.Find the value of x² + 2xy + y² when x = 15 and y = 11.
14. 14.Use (a − b)² = a² − 2ab + b² to find 12².
15. 15.Use (a + b)(a − b) = a² − b² to find 88 × 72.
16. 16.If a − b = 2 and ab = 15, what is a² + b²?
17. 17.Use (a + b)² = a² + 2ab + b² to find 77².
18. 18.Use (a + b)(a − b) = a² − b² to find 49 × 31.
19. 19.Use (a + b)² = a² + 2ab + b² to find 46².
20. 20.Find the value of x² + 2xy + y² when x = 9 and y = 2.
21. 21.Use a² − b² = (a + b)(a − b) to find 27² − 8².
22. 22.Find the value of x² − 2xy + y² when x = 4 and y = 1.
23. 23.Use (a + b)² = a² + 2ab + b² to find 94².
24. 24.Find the value of x² + 2xy + y² when x = 9 and y = 4.
25. 25.Find the value of x² + 2xy + y² when x = 13 and y = 4.
26. 26.Find the value of x² − 2xy + y² when x = 14 and y = 3.
27. 27.If a − b = 2 and ab = 63, what is a² + b²?
28. 28.Use a² − b² = (a + b)(a − b) to find 28² − 5².
29. 29.Use (a + b)² = a² + 2ab + b² to find 64².
30. 30.Use (a + b)² = a² + 2ab + b² to find 21².
31. 31.If a + b = 9 and ab = 20, what is a² + b²?
32. 32.Use (a + b)² = a² + 2ab + b² to find 14².
33. 33.Use (a + b)² = a² + 2ab + b² to find 34².
34. 34.Use (a + b)² = a² + 2ab + b² to find 69².
35. 35.Find the value of x² + 2xy + y² when x = 8 and y = 7.
36. 36.Use a² − b² = (a + b)(a − b) to find 95² − 26².
37. 37.Use (a + b)² = a² + 2ab + b² to find 44².
38. 38.Use a² − b² = (a + b)(a − b) to find 36² − 7².
39. 39.If a − b = 3 and ab = 70, what is a² + b²?
40. 40.Use (a + b)² = a² + 2ab + b² to find 19².

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