Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 53 · 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 49².
2. 2.Use a² − b² = (a + b)(a − b) to find 20² − 1².
3. 3.Find the value of x² + 2xy + y² when x = 10 and y = 1.
4. 4.Use a² − b² = (a + b)(a − b) to find 96² − 1².
5. 5.Use (a + b)(a − b) = a² − b² to find 98 × 82.
6. 6.Use (a + b)² = a² + 2ab + b² to find 95².
7. 7.Use (a + b)² = a² + 2ab + b² to find 93².
8. 8.If a + b = 6 and ab = 5, what is a² + b²?
9. 9.Use a² − b² = (a + b)(a − b) to find 91² − 48².
10. 10.Use a² − b² = (a + b)(a − b) to find 85² − 7².
11. 11.Use (a + b)² = a² + 2ab + b² to find 19².
12. 12.Use (a + b)(a − b) = a² − b² to find 36 × 24.
13. 13.Use (a + b)² = a² + 2ab + b² to find 106².
14. 14.If a + b = 15 and ab = 36, what is a² + b²?
15. 15.Use (a + b)(a − b) = a² − b² to find 63 × 57.
16. 16.Use (a − b)² = a² − 2ab + b² to find 97².
17. 17.Use (a + b)² = a² + 2ab + b² to find 26².
18. 18.Use (a + b)² = a² + 2ab + b² to find 13².
19. 19.Use a² − b² = (a + b)(a − b) to find 95² − 77².
20. 20.Use (a + b)² = a² + 2ab + b² to find 101².
21. 21.If a − b = 2 and ab = 15, what is a² + b²?
22. 22.Find the value of x² − y² when x = 5 and y = 1.
23. 23.Use a² − b² = (a + b)(a − b) to find 97² − 69².
24. 24.Use (a − b)² = a² − 2ab + b² to find 52².
25. 25.Use a² − b² = (a + b)(a − b) to find 47² − 32².
26. 26.If a − b = 10 and ab = 11, what is a² + b²?
27. 27.Find the value of x² + 2xy + y² when x = 3 and y = 1.
28. 28.Find the value of x² + 2xy + y² when x = 12 and y = 1.
29. 29.Use a² − b² = (a + b)(a − b) to find 40² − 15².
30. 30.Use (a + b)² = a² + 2ab + b² to find 84².
31. 31.Find the value of x² + 2xy + y² when x = 4 and y = 1.
32. 32.Use (a − b)² = a² − 2ab + b² to find 16².
33. 33.Use (a − b)² = a² − 2ab + b² to find 35².
34. 34.Use (a + b)² = a² + 2ab + b² to find 11².
35. 35.Use (a + b)(a − b) = a² − b² to find 49 × 31.
36. 36.Find the value of x² − 2xy + y² when x = 9 and y = 2.
37. 37.If a − b = 8 and ab = 9, what is a² + b²?
38. 38.Find the value of x² + 2xy + y² when x = 13 and y = 8.
39. 39.Use a² − b² = (a + b)(a − b) to find 95² − 4².
40. 40.Use (a − b)² = a² − 2ab + b² to find 23².

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