Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 680 · 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.If a − b = 1 and ab = 6, what is a² + b²?
2. 2.Find the value of x² − 2xy + y² when x = 15 and y = 9.
3. 3.Use (a − b)² = a² − 2ab + b² to find 23².
4. 4.Use (a + b)² = a² + 2ab + b² to find 41².
5. 5.Find the value of x² − y² when x = 10 and y = 6.
6. 6.Find the value of x² + 2xy + y² when x = 14 and y = 2.
7. 7.Use a² − b² = (a + b)(a − b) to find 49² − 5².
8. 8.Use (a − b)² = a² − 2ab + b² to find 63².
9. 9.Use (a + b)(a − b) = a² − b² to find 88 × 72.
10. 10.Use (a − b)² = a² − 2ab + b² to find 56².
11. 11.Find the value of x² + 2xy + y² when x = 3 and y = 2.
12. 12.Use (a + b)(a − b) = a² − b² to find 73 × 67.
13. 13.Use (a − b)² = a² − 2ab + b² to find 89².
14. 14.Use (a + b)(a − b) = a² − b² to find 24 × 16.
15. 15.Use (a + b)(a − b) = a² − b² to find 62 × 58.
16. 16.Find the value of x² − y² when x = 7 and y = 3.
17. 17.Use (a + b)(a − b) = a² − b² to find 109 × 91.
18. 18.Use (a − b)² = a² − 2ab + b² to find 55².
19. 19.Find the value of x² − y² when x = 7 and y = 6.
20. 20.If a − b = 2 and ab = 24, what is a² + b²?
21. 21.Use (a + b)(a − b) = a² − b² to find 92 × 88.
22. 22.Use (a + b)(a − b) = a² − b² to find 97 × 83.
23. 23.Use (a − b)² = a² − 2ab + b² to find 78².
24. 24.Use (a + b)(a − b) = a² − b² to find 29 × 11.
25. 25.If a − b = 3 and ab = 10, what is a² + b²?
26. 26.If a + b = 12 and ab = 35, what is a² + b²?
27. 27.If a + b = 13 and ab = 30, what is a² + b²?
28. 28.Use (a − b)² = a² − 2ab + b² to find 86².
29. 29.Use (a − b)² = a² − 2ab + b² to find 54².
30. 30.Use (a − b)² = a² − 2ab + b² to find 67².
31. 31.Use a² − b² = (a + b)(a − b) to find 84² − 2².
32. 32.Use (a + b)(a − b) = a² − b² to find 51 × 49.
33. 33.Use (a + b)² = a² + 2ab + b² to find 68².
34. 34.Find the value of x² + 2xy + y² when x = 9 and y = 7.
35. 35.Use a² − b² = (a + b)(a − b) to find 89² − 7².
36. 36.Find the value of x² − 2xy + y² when x = 14 and y = 12.
37. 37.Use (a + b)² = a² + 2ab + b² to find 89².
38. 38.If a + b = 10 and ab = 24, what is a² + b²?
39. 39.Use (a + b)² = a² + 2ab + b² to find 91².
40. 40.Use (a − b)² = a² − 2ab + b² to find 58².

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