Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 833 · 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 68².
2. 2.If a + b = 7 and ab = 10, what is a² + b²?
3. 3.Use (a − b)² = a² − 2ab + b² to find 24².
4. 4.Use (a + b)² = a² + 2ab + b² to find 42².
5. 5.If a − b = 1 and ab = 20, what is a² + b²?
6. 6.Use (a + b)² = a² + 2ab + b² to find 93².
7. 7.Find the value of x² − 2xy + y² when x = 13 and y = 6.
8. 8.Use (a + b)² = a² + 2ab + b² to find 91².
9. 9.Use a² − b² = (a + b)(a − b) to find 79² − 4².
10. 10.Use a² − b² = (a + b)(a − b) to find 89² − 84².
11. 11.Use (a − b)² = a² − 2ab + b² to find 37².
12. 12.If a − b = 4 and ab = 45, what is a² + b²?
13. 13.Use a² − b² = (a + b)(a − b) to find 36² − 23².
14. 14.Use (a − b)² = a² − 2ab + b² to find 21².
15. 15.Use (a + b)² = a² + 2ab + b² to find 75².
16. 16.Use (a + b)(a − b) = a² − b² to find 67 × 53.
17. 17.If a + b = 6 and ab = 5, what is a² + b²?
18. 18.Find the value of x² − 2xy + y² when x = 5 and y = 1.
19. 19.If a − b = 4 and ab = 12, what is a² + b²?
20. 20.Find the value of x² − y² when x = 11 and y = 2.
21. 21.Use a² − b² = (a + b)(a − b) to find 87² − 71².
22. 22.Use (a − b)² = a² − 2ab + b² to find 12².
23. 23.If a − b = 1 and ab = 2, what is a² + b²?
24. 24.Use (a − b)² = a² − 2ab + b² to find 79².
25. 25.Use (a + b)² = a² + 2ab + b² to find 71².
26. 26.Use (a + b)(a − b) = a² − b² to find 84 × 76.
27. 27.Find the value of x² − 2xy + y² when x = 9 and y = 3.
28. 28.If a + b = 5 and ab = 6, what is a² + b²?
29. 29.Use (a + b)² = a² + 2ab + b² to find 63².
30. 30.If a + b = 13 and ab = 36, what is a² + b²?
31. 31.Use (a + b)(a − b) = a² − b² to find 26 × 14.
32. 32.Use (a − b)² = a² − 2ab + b² to find 72².
33. 33.Use a² − b² = (a + b)(a − b) to find 78² − 66².
34. 34.Use (a + b)(a − b) = a² − b² to find 45 × 35.
35. 35.Use (a − b)² = a² − 2ab + b² to find 73².
36. 36.Use (a + b)² = a² + 2ab + b² to find 13².
37. 37.Use (a + b)² = a² + 2ab + b² to find 27².
38. 38.Use (a + b)² = a² + 2ab + b² to find 12².
39. 39.Find the value of x² − y² when x = 4 and y = 2.
40. 40.Use (a − b)² = a² − 2ab + b² to find 41².

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