Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 204 · 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 97².
2. 2.Use (a + b)² = a² + 2ab + b² to find 41².
3. 3.Use a² − b² = (a + b)(a − b) to find 96² − 8².
4. 4.Use (a + b)(a − b) = a² − b² to find 53 × 47.
5. 5.Find the value of x² + 2xy + y² when x = 14 and y = 2.
6. 6.Find the value of x² − 2xy + y² when x = 11 and y = 1.
7. 7.If a + b = 7 and ab = 12, what is a² + b²?
8. 8.Use (a + b)² = a² + 2ab + b² to find 102².
9. 9.Use a² − b² = (a + b)(a − b) to find 20² − 5².
10. 10.Find the value of x² + 2xy + y² when x = 5 and y = 4.
11. 11.If a − b = 2 and ab = 48, what is a² + b²?
12. 12.Find the value of x² − 2xy + y² when x = 13 and y = 2.
13. 13.Use a² − b² = (a + b)(a − b) to find 70² − 57².
14. 14.Use (a − b)² = a² − 2ab + b² to find 11².
15. 15.Use (a + b)(a − b) = a² − b² to find 84 × 76.
16. 16.Use (a + b)(a − b) = a² − b² to find 67 × 53.
17. 17.Find the value of x² − 2xy + y² when x = 9 and y = 8.
18. 18.Find the value of x² + 2xy + y² when x = 12 and y = 2.
19. 19.Use (a + b)² = a² + 2ab + b² to find 12².
20. 20.Use (a + b)² = a² + 2ab + b² to find 98².
21. 21.Use (a + b)(a − b) = a² − b² to find 49 × 31.
22. 22.Use (a + b)² = a² + 2ab + b² to find 29².
23. 23.If a + b = 14 and ab = 40, what is a² + b²?
24. 24.Use a² − b² = (a + b)(a − b) to find 27² − 13².
25. 25.Use (a − b)² = a² − 2ab + b² to find 43².
26. 26.Use (a + b)(a − b) = a² − b² to find 88 × 72.
27. 27.If a + b = 9 and ab = 8, what is a² + b²?
28. 28.Use (a − b)² = a² − 2ab + b² to find 18².
29. 29.Use (a + b)² = a² + 2ab + b² to find 68².
30. 30.If a + b = 16 and ab = 48, what is a² + b²?
31. 31.Use (a − b)² = a² − 2ab + b² to find 45².
32. 32.Use a² − b² = (a + b)(a − b) to find 76² − 33².
33. 33.Use a² − b² = (a + b)(a − b) to find 91² − 21².
34. 34.If a − b = 3 and ab = 28, what is a² + b²?
35. 35.Use (a + b)² = a² + 2ab + b² to find 81².
36. 36.Use (a + b)² = a² + 2ab + b² to find 13².
37. 37.Use (a + b)(a − b) = a² − b² to find 57 × 43.
38. 38.Use (a − b)² = a² − 2ab + b² to find 52².
39. 39.Use a² − b² = (a + b)(a − b) to find 63² − 51².
40. 40.Use (a + b)(a − b) = a² − b² to find 106 × 94.

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