Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 192 · 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 45² − 26².
2. 2.Use (a + b)² = a² + 2ab + b² to find 64².
3. 3.If a − b = 8 and ab = 48, what is a² + b²?
4. 4.Use a² − b² = (a + b)(a − b) to find 92² − 22².
5. 5.Use (a − b)² = a² − 2ab + b² to find 62².
6. 6.Use (a + b)² = a² + 2ab + b² to find 104².
7. 7.Use (a + b)(a − b) = a² − b² to find 75 × 65.
8. 8.Find the value of x² − 2xy + y² when x = 11 and y = 10.
9. 9.Use (a + b)² = a² + 2ab + b² to find 31².
10. 10.If a − b = 1 and ab = 72, what is a² + b²?
11. 11.Use (a − b)² = a² − 2ab + b² to find 19².
12. 12.Use (a + b)(a − b) = a² − b² to find 63 × 57.
13. 13.Use (a + b)² = a² + 2ab + b² to find 106².
14. 14.Find the value of x² + 2xy + y² when x = 3 and y = 1.
15. 15.Use (a − b)² = a² − 2ab + b² to find 31².
16. 16.Use (a − b)² = a² − 2ab + b² to find 66².
17. 17.Use (a + b)(a − b) = a² − b² to find 22 × 18.
18. 18.Use (a + b)(a − b) = a² − b² to find 27 × 13.
19. 19.Use (a + b)² = a² + 2ab + b² to find 18².
20. 20.Use (a + b)(a − b) = a² − b² to find 31 × 29.
21. 21.Use (a + b)(a − b) = a² − b² to find 61 × 59.
22. 22.Find the value of x² + 2xy + y² when x = 11 and y = 8.
23. 23.Use a² − b² = (a + b)(a − b) to find 93² − 8².
24. 24.Use (a − b)² = a² − 2ab + b² to find 42².
25. 25.Use a² − b² = (a + b)(a − b) to find 55² − 49².
26. 26.Find the value of x² + 2xy + y² when x = 13 and y = 10.
27. 27.Use (a − b)² = a² − 2ab + b² to find 32².
28. 28.Use (a + b)² = a² + 2ab + b² to find 58².
29. 29.Use a² − b² = (a + b)(a − b) to find 26² − 22².
30. 30.If a − b = 3 and ab = 108, what is a² + b²?
31. 31.Use (a + b)(a − b) = a² − b² to find 98 × 82.
32. 32.Use (a − b)² = a² − 2ab + b² to find 25².
33. 33.If a + b = 7 and ab = 12, what is a² + b²?
34. 34.If a + b = 5 and ab = 6, what is a² + b²?
35. 35.Use (a + b)² = a² + 2ab + b² to find 102².
36. 36.Use (a − b)² = a² − 2ab + b² to find 91².
37. 37.Use (a + b)² = a² + 2ab + b² to find 24².
38. 38.Use (a + b)(a − b) = a² − b² to find 43 × 37.
39. 39.Use a² − b² = (a + b)(a − b) to find 26² − 3².
40. 40.Use a² − b² = (a + b)(a − b) to find 84² − 21².

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