Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 611 · 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 77².
2. 2.Use (a + b)(a − b) = a² − b² to find 101 × 99.
3. 3.Use a² − b² = (a + b)(a − b) to find 73² − 29².
4. 4.If a − b = 1 and ab = 12, what is a² + b²?
5. 5.Use (a + b)² = a² + 2ab + b² to find 42².
6. 6.Use (a + b)² = a² + 2ab + b² to find 76².
7. 7.Find the value of x² − y² when x = 3 and y = 1.
8. 8.Use (a + b)(a − b) = a² − b² to find 41 × 39.
9. 9.Use a² − b² = (a + b)(a − b) to find 73² − 63².
10. 10.If a − b = 2 and ab = 15, what is a² + b²?
11. 11.Find the value of x² − y² when x = 8 and y = 3.
12. 12.Use (a + b)² = a² + 2ab + b² to find 11².
13. 13.If a + b = 18 and ab = 80, what is a² + b²?
14. 14.Use a² − b² = (a + b)(a − b) to find 95² − 77².
15. 15.Use a² − b² = (a + b)(a − b) to find 68² − 34².
16. 16.Use a² − b² = (a + b)(a − b) to find 22² − 20².
17. 17.Find the value of x² + 2xy + y² when x = 11 and y = 1.
18. 18.Find the value of x² − y² when x = 14 and y = 12.
19. 19.Use a² − b² = (a + b)(a − b) to find 52² − 14².
20. 20.Use (a + b)² = a² + 2ab + b² to find 32².
21. 21.Use (a + b)² = a² + 2ab + b² to find 41².
22. 22.Use a² − b² = (a + b)(a − b) to find 50² − 45².
23. 23.Use (a + b)² = a² + 2ab + b² to find 66².
24. 24.Use (a + b)(a − b) = a² − b² to find 36 × 24.
25. 25.Use (a − b)² = a² − 2ab + b² to find 27².
26. 26.Use (a + b)(a − b) = a² − b² to find 78 × 62.
27. 27.Use (a − b)² = a² − 2ab + b² to find 66².
28. 28.Use (a + b)² = a² + 2ab + b² to find 33².
29. 29.Use (a + b)² = a² + 2ab + b² to find 99².
30. 30.Use (a + b)² = a² + 2ab + b² to find 12².
31. 31.Find the value of x² − 2xy + y² when x = 10 and y = 5.
32. 32.Use a² − b² = (a + b)(a − b) to find 43² − 22².
33. 33.Use (a − b)² = a² − 2ab + b² to find 11².
34. 34.Use a² − b² = (a + b)(a − b) to find 38² − 4².
35. 35.Use a² − b² = (a + b)(a − b) to find 65² − 46².
36. 36.Use a² − b² = (a + b)(a − b) to find 69² − 59².
37. 37.Use (a + b)² = a² + 2ab + b² to find 35².
38. 38.Use a² − b² = (a + b)(a − b) to find 63² − 25².
39. 39.Use (a + b)² = a² + 2ab + b² to find 21².
40. 40.Use a² − b² = (a + b)(a − b) to find 69² − 44².

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