Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 393 · 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 54².
2. 2.Use (a + b)² = a² + 2ab + b² to find 49².
3. 3.Use (a + b)(a − b) = a² − b² to find 31 × 29.
4. 4.Use (a − b)² = a² − 2ab + b² to find 75².
5. 5.Find the value of x² − y² when x = 5 and y = 1.
6. 6.Use a² − b² = (a + b)(a − b) to find 32² − 30².
7. 7.Use (a + b)² = a² + 2ab + b² to find 77².
8. 8.Use (a + b)² = a² + 2ab + b² to find 21².
9. 9.Use (a + b)² = a² + 2ab + b² to find 75².
10. 10.Find the value of x² − y² when x = 12 and y = 7.
11. 11.Use (a − b)² = a² − 2ab + b² to find 61².
12. 12.Use a² − b² = (a + b)(a − b) to find 43² − 26².
13. 13.If a + b = 5 and ab = 4, what is a² + b²?
14. 14.Use (a + b)² = a² + 2ab + b² to find 104².
15. 15.If a − b = 1 and ab = 2, what is a² + b²?
16. 16.If a + b = 12 and ab = 20, what is a² + b²?
17. 17.Find the value of x² − 2xy + y² when x = 4 and y = 1.
18. 18.Use a² − b² = (a + b)(a − b) to find 36² − 11².
19. 19.Use (a + b)² = a² + 2ab + b² to find 98².
20. 20.Use a² − b² = (a + b)(a − b) to find 40² − 4².
21. 21.Use (a − b)² = a² − 2ab + b² to find 66².
22. 22.Use (a + b)² = a² + 2ab + b² to find 16².
23. 23.Find the value of x² − 2xy + y² when x = 3 and y = 1.
24. 24.Use (a + b)² = a² + 2ab + b² to find 24².
25. 25.Use (a + b)² = a² + 2ab + b² to find 45².
26. 26.Use (a + b)(a − b) = a² − b² to find 43 × 37.
27. 27.Find the value of x² − y² when x = 13 and y = 12.
28. 28.Use a² − b² = (a + b)(a − b) to find 84² − 66².
29. 29.Use (a − b)² = a² − 2ab + b² to find 48².
30. 30.Use (a + b)² = a² + 2ab + b² to find 81².
31. 31.Use (a − b)² = a² − 2ab + b² to find 23².
32. 32.If a − b = 8 and ab = 9, what is a² + b²?
33. 33.Find the value of x² + 2xy + y² when x = 13 and y = 7.
34. 34.Use (a + b)(a − b) = a² − b² to find 107 × 93.
35. 35.Use (a + b)² = a² + 2ab + b² to find 94².
36. 36.If a + b = 4 and ab = 3, what is a² + b²?
37. 37.Use (a + b)² = a² + 2ab + b² to find 61².
38. 38.Use (a + b)² = a² + 2ab + b² to find 92².
39. 39.Use (a − b)² = a² − 2ab + b² to find 93².
40. 40.Use (a − b)² = a² − 2ab + b² to find 35².

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