Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 729 · 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 95² − 85².
2. 2.Use (a + b)² = a² + 2ab + b² to find 25².
3. 3.Use (a + b)(a − b) = a² − b² to find 57 × 43.
4. 4.Use (a + b)(a − b) = a² − b² to find 22 × 18.
5. 5.Use (a + b)² = a² + 2ab + b² to find 106².
6. 6.Find the value of x² − 2xy + y² when x = 11 and y = 3.
7. 7.Find the value of x² + 2xy + y² when x = 10 and y = 8.
8. 8.Use (a + b)(a − b) = a² − b² to find 66 × 54.
9. 9.Use a² − b² = (a + b)(a − b) to find 54² − 4².
10. 10.Use a² − b² = (a + b)(a − b) to find 27² − 4².
11. 11.Use a² − b² = (a + b)(a − b) to find 99² − 4².
12. 12.Use (a + b)² = a² + 2ab + b² to find 51².
13. 13.Use (a + b)(a − b) = a² − b² to find 32 × 28.
14. 14.Use (a + b)² = a² + 2ab + b² to find 45².
15. 15.If a + b = 19 and ab = 90, what is a² + b²?
16. 16.Use a² − b² = (a + b)(a − b) to find 98² − 30².
17. 17.Use a² − b² = (a + b)(a − b) to find 88² − 35².
18. 18.Use a² − b² = (a + b)(a − b) to find 39² − 29².
19. 19.Use (a + b)² = a² + 2ab + b² to find 69².
20. 20.Use (a + b)² = a² + 2ab + b² to find 107².
21. 21.Use a² − b² = (a + b)(a − b) to find 45² − 1².
22. 22.If a + b = 11 and ab = 18, what is a² + b²?
23. 23.Use (a + b)² = a² + 2ab + b² to find 28².
24. 24.Use a² − b² = (a + b)(a − b) to find 68² − 56².
25. 25.Use a² − b² = (a + b)(a − b) to find 66² − 62².
26. 26.Use (a + b)(a − b) = a² − b² to find 33 × 27.
27. 27.Use (a + b)(a − b) = a² − b² to find 44 × 36.
28. 28.Use (a + b)(a − b) = a² − b² to find 54 × 46.
29. 29.If a + b = 11 and ab = 28, what is a² + b²?
30. 30.Use (a + b)(a − b) = a² − b² to find 98 × 82.
31. 31.Use (a + b)(a − b) = a² − b² to find 21 × 19.
32. 32.Use (a − b)² = a² − 2ab + b² to find 86².
33. 33.If a − b = 3 and ab = 54, what is a² + b²?
34. 34.Find the value of x² + 2xy + y² when x = 13 and y = 4.
35. 35.Use (a + b)² = a² + 2ab + b² to find 91².
36. 36.Use (a + b)(a − b) = a² − b² to find 31 × 29.
37. 37.Use (a + b)² = a² + 2ab + b² to find 54².
38. 38.Use (a + b)² = a² + 2ab + b² to find 27².
39. 39.If a + b = 21 and ab = 108, what is a² + b²?
40. 40.If a + b = 18 and ab = 72, what is a² + b²?

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