Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 11 · 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 = 2 and ab = 8, what is a² + b²?
2. 2.Use (a − b)² = a² − 2ab + b² to find 58².
3. 3.If a + b = 16 and ab = 55, what is a² + b²?
4. 4.Use (a + b)(a − b) = a² − b² to find 99 × 81.
5. 5.Use a² − b² = (a + b)(a − b) to find 74² − 10².
6. 6.If a − b = 4 and ab = 32, what is a² + b²?
7. 7.Use (a − b)² = a² − 2ab + b² to find 95².
8. 8.If a + b = 20 and ab = 96, what is a² + b²?
9. 9.Use a² − b² = (a + b)(a − b) to find 68² − 4².
10. 10.If a + b = 7 and ab = 10, what is a² + b²?
11. 11.Use (a − b)² = a² − 2ab + b² to find 52².
12. 12.Use a² − b² = (a + b)(a − b) to find 68² − 47².
13. 13.Use (a − b)² = a² − 2ab + b² to find 42².
14. 14.Use a² − b² = (a + b)(a − b) to find 81² − 11².
15. 15.Use (a + b)(a − b) = a² − b² to find 48 × 32.
16. 16.Use (a − b)² = a² − 2ab + b² to find 64².
17. 17.Use (a + b)(a − b) = a² − b² to find 29 × 11.
18. 18.If a + b = 11 and ab = 10, what is a² + b²?
19. 19.If a − b = 1 and ab = 90, what is a² + b²?
20. 20.Use a² − b² = (a + b)(a − b) to find 75² − 25².
21. 21.Use a² − b² = (a + b)(a − b) to find 66² − 51².
22. 22.Use (a + b)(a − b) = a² − b² to find 37 × 23.
23. 23.Find the value of x² − 2xy + y² when x = 9 and y = 1.
24. 24.Find the value of x² − y² when x = 11 and y = 5.
25. 25.Use a² − b² = (a + b)(a − b) to find 45² − 3².
26. 26.If a + b = 13 and ab = 30, what is a² + b²?
27. 27.Find the value of x² − 2xy + y² when x = 6 and y = 2.
28. 28.Find the value of x² − 2xy + y² when x = 11 and y = 1.
29. 29.If a − b = 2 and ab = 3, what is a² + b²?
30. 30.If a − b = 3 and ab = 10, what is a² + b²?
31. 31.Use (a − b)² = a² − 2ab + b² to find 98².
32. 32.Use (a − b)² = a² − 2ab + b² to find 37².
33. 33.Use (a + b)(a − b) = a² − b² to find 81 × 79.
34. 34.Find the value of x² − y² when x = 9 and y = 1.
35. 35.If a + b = 14 and ab = 45, what is a² + b²?
36. 36.Find the value of x² − 2xy + y² when x = 15 and y = 4.
37. 37.If a + b = 16 and ab = 48, what is a² + b²?
38. 38.Use (a + b)² = a² + 2ab + b² to find 75².
39. 39.Use a² − b² = (a + b)(a − b) to find 92² − 66².
40. 40.Use a² − b² = (a + b)(a − b) to find 20² − 18².

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