Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 546 · 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 a² − b² = (a + b)(a − b) to find 47² − 17².
2. 2.Use a² − b² = (a + b)(a − b) to find 81² − 3².
3. 3.Find the value of x² − 2xy + y² when x = 4 and y = 2.
4. 4.Use (a − b)² = a² − 2ab + b² to find 79².
5. 5.Use (a + b)(a − b) = a² − b² to find 98 × 82.
6. 6.Use (a + b)² = a² + 2ab + b² to find 68².
7. 7.If a − b = 1 and ab = 2, what is a² + b²?
8. 8.Use a² − b² = (a + b)(a − b) to find 50² − 14².
9. 9.Use (a + b)² = a² + 2ab + b² to find 24².
10. 10.Use (a + b)² = a² + 2ab + b² to find 25².
11. 11.Find the value of x² + 2xy + y² when x = 5 and y = 4.
12. 12.Use a² − b² = (a + b)(a − b) to find 32² − 13².
13. 13.Use (a − b)² = a² − 2ab + b² to find 19².
14. 14.Use (a − b)² = a² − 2ab + b² to find 17².
15. 15.Use (a − b)² = a² − 2ab + b² to find 45².
16. 16.Use (a + b)(a − b) = a² − b² to find 109 × 91.
17. 17.Use a² − b² = (a + b)(a − b) to find 75² − 61².
18. 18.Use (a − b)² = a² − 2ab + b² to find 39².
19. 19.Use (a − b)² = a² − 2ab + b² to find 99².
20. 20.Find the value of x² − y² when x = 11 and y = 6.
21. 21.Use (a + b)² = a² + 2ab + b² to find 22².
22. 22.Find the value of x² − y² when x = 4 and y = 1.
23. 23.Use a² − b² = (a + b)(a − b) to find 43² − 2².
24. 24.Use (a + b)(a − b) = a² − b² to find 58 × 42.
25. 25.Use (a − b)² = a² − 2ab + b² to find 77².
26. 26.Find the value of x² − 2xy + y² when x = 9 and y = 7.
27. 27.Find the value of x² − y² when x = 5 and y = 1.
28. 28.Use (a + b)(a − b) = a² − b² to find 51 × 49.
29. 29.Use (a + b)(a − b) = a² − b² to find 43 × 37.
30. 30.Use (a + b)² = a² + 2ab + b² to find 91².
31. 31.Use (a − b)² = a² − 2ab + b² to find 15².
32. 32.If a + b = 8 and ab = 15, what is a² + b²?
33. 33.Use (a − b)² = a² − 2ab + b² to find 33².
34. 34.Find the value of x² + 2xy + y² when x = 12 and y = 8.
35. 35.Use (a − b)² = a² − 2ab + b² to find 24².
36. 36.Use (a + b)² = a² + 2ab + b² to find 31².
37. 37.Use a² − b² = (a + b)(a − b) to find 77² − 19².
38. 38.Use (a + b)(a − b) = a² − b² to find 47 × 33.
39. 39.Use (a + b)² = a² + 2ab + b² to find 76².
40. 40.If a + b = 7 and ab = 12, what is a² + b²?

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