Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 61 · 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 91².
2. 2.Find the value of x² − 2xy + y² when x = 10 and y = 2.
3. 3.Use (a + b)(a − b) = a² − b² to find 76 × 64.
4. 4.Use (a + b)(a − b) = a² − b² to find 65 × 55.
5. 5.Use (a + b)(a − b) = a² − b² to find 54 × 46.
6. 6.Use (a + b)² = a² + 2ab + b² to find 11².
7. 7.If a − b = 5 and ab = 14, what is a² + b²?
8. 8.Use (a − b)² = a² − 2ab + b² to find 93².
9. 9.Use a² − b² = (a + b)(a − b) to find 91² − 2².
10. 10.Use (a − b)² = a² − 2ab + b² to find 46².
11. 11.Use (a + b)² = a² + 2ab + b² to find 87².
12. 12.Use (a + b)² = a² + 2ab + b² to find 102².
13. 13.Use a² − b² = (a + b)(a − b) to find 43² − 4².
14. 14.Use (a + b)(a − b) = a² − b² to find 46 × 34.
15. 15.If a − b = 2 and ab = 8, what is a² + b²?
16. 16.Use (a + b)² = a² + 2ab + b² to find 86².
17. 17.Use (a − b)² = a² − 2ab + b² to find 45².
18. 18.Use a² − b² = (a + b)(a − b) to find 56² − 24².
19. 19.If a − b = 3 and ab = 10, what is a² + b²?
20. 20.Use (a + b)(a − b) = a² − b² to find 102 × 98.
21. 21.Use (a + b)² = a² + 2ab + b² to find 61².
22. 22.Use (a − b)² = a² − 2ab + b² to find 79².
23. 23.Find the value of x² − 2xy + y² when x = 15 and y = 6.
24. 24.Use (a + b)(a − b) = a² − b² to find 53 × 47.
25. 25.If a + b = 10 and ab = 16, what is a² + b²?
26. 26.If a + b = 6 and ab = 8, what is a² + b²?
27. 27.Use (a + b)(a − b) = a² − b² to find 84 × 76.
28. 28.Find the value of x² − y² when x = 7 and y = 6.
29. 29.Use (a + b)(a − b) = a² − b² to find 99 × 81.
30. 30.If a − b = 1 and ab = 132, what is a² + b²?
31. 31.Find the value of x² − y² when x = 13 and y = 2.
32. 32.Use a² − b² = (a + b)(a − b) to find 58² − 41².
33. 33.If a + b = 10 and ab = 9, what is a² + b²?
34. 34.Find the value of x² − 2xy + y² when x = 7 and y = 3.
35. 35.If a − b = 7 and ab = 18, what is a² + b²?
36. 36.Use (a − b)² = a² − 2ab + b² to find 85².
37. 37.If a − b = 2 and ab = 3, what is a² + b²?
38. 38.Find the value of x² − 2xy + y² when x = 5 and y = 3.
39. 39.Use (a + b)² = a² + 2ab + b² to find 94².
40. 40.Use (a − b)² = a² − 2ab + b² to find 57².

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