Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 484 · 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)(a − b) = a² − b² to find 28 × 12.
2. 2.Use a² − b² = (a + b)(a − b) to find 61² − 43².
3. 3.Use (a + b)(a − b) = a² − b² to find 58 × 42.
4. 4.Use (a − b)² = a² − 2ab + b² to find 26².
5. 5.If a − b = 4 and ab = 21, what is a² + b²?
6. 6.Use (a − b)² = a² − 2ab + b² to find 88².
7. 7.Use (a + b)(a − b) = a² − b² to find 41 × 39.
8. 8.Use (a − b)² = a² − 2ab + b² to find 49².
9. 9.Use (a − b)² = a² − 2ab + b² to find 48².
10. 10.Use (a + b)² = a² + 2ab + b² to find 38².
11. 11.Use (a + b)(a − b) = a² − b² to find 51 × 49.
12. 12.Use a² − b² = (a + b)(a − b) to find 85² − 7².
13. 13.Use (a − b)² = a² − 2ab + b² to find 45².
14. 14.Use a² − b² = (a + b)(a − b) to find 93² − 8².
15. 15.Use (a + b)² = a² + 2ab + b² to find 14².
16. 16.Use a² − b² = (a + b)(a − b) to find 52² − 8².
17. 17.If a − b = 2 and ab = 80, what is a² + b²?
18. 18.Use (a + b)(a − b) = a² − b² to find 82 × 78.
19. 19.Use (a + b)(a − b) = a² − b² to find 62 × 58.
20. 20.If a − b = 6 and ab = 7, what is a² + b²?
21. 21.If a − b = 2 and ab = 3, what is a² + b²?
22. 22.Use (a + b)(a − b) = a² − b² to find 78 × 62.
23. 23.Find the value of x² + 2xy + y² when x = 10 and y = 6.
24. 24.Use (a − b)² = a² − 2ab + b² to find 73².
25. 25.Find the value of x² − 2xy + y² when x = 8 and y = 4.
26. 26.Use (a − b)² = a² − 2ab + b² to find 15².
27. 27.Use a² − b² = (a + b)(a − b) to find 22² − 1².
28. 28.Use (a + b)(a − b) = a² − b² to find 77 × 63.
29. 29.Use a² − b² = (a + b)(a − b) to find 80² − 13².
30. 30.If a + b = 4 and ab = 3, what is a² + b²?
31. 31.Use (a + b)² = a² + 2ab + b² to find 13².
32. 32.Use a² − b² = (a + b)(a − b) to find 37² − 8².
33. 33.If a + b = 12 and ab = 32, what is a² + b²?
34. 34.If a + b = 12 and ab = 11, what is a² + b²?
35. 35.Find the value of x² − 2xy + y² when x = 12 and y = 10.
36. 36.Use (a + b)² = a² + 2ab + b² to find 29².
37. 37.Use (a − b)² = a² − 2ab + b² to find 21².
38. 38.Find the value of x² − y² when x = 11 and y = 10.
39. 39.Find the value of x² − y² when x = 7 and y = 5.
40. 40.Use (a + b)² = a² + 2ab + b² to find 57².

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