Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 957 · 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)(a − b) = a² − b² to find 107 × 93.
2. 2.If a − b = 5 and ab = 84, what is a² + b²?
3. 3.Use (a + b)(a − b) = a² − b² to find 41 × 39.
4. 4.Find the value of x² − 2xy + y² when x = 10 and y = 4.
5. 5.Use (a − b)² = a² − 2ab + b² to find 34².
6. 6.Use (a + b)(a − b) = a² − b² to find 83 × 77.
7. 7.Find the value of x² + 2xy + y² when x = 3 and y = 1.
8. 8.Use (a + b)(a − b) = a² − b² to find 34 × 26.
9. 9.If a + b = 19 and ab = 84, what is a² + b²?
10. 10.Find the value of x² + 2xy + y² when x = 15 and y = 2.
11. 11.Use (a + b)² = a² + 2ab + b² to find 72².
12. 12.Find the value of x² + 2xy + y² when x = 9 and y = 5.
13. 13.Find the value of x² − y² when x = 12 and y = 10.
14. 14.Use a² − b² = (a + b)(a − b) to find 29² − 18².
15. 15.Use (a + b)² = a² + 2ab + b² to find 61².
16. 16.Use (a + b)² = a² + 2ab + b² to find 24².
17. 17.Use (a + b)(a − b) = a² − b² to find 65 × 55.
18. 18.Use a² − b² = (a + b)(a − b) to find 51² − 32².
19. 19.Use (a − b)² = a² − 2ab + b² to find 76².
20. 20.Use (a + b)(a − b) = a² − b² to find 109 × 91.
21. 21.Use (a + b)(a − b) = a² − b² to find 82 × 78.
22. 22.Use (a + b)(a − b) = a² − b² to find 53 × 47.
23. 23.Use a² − b² = (a + b)(a − b) to find 29² − 1².
24. 24.Use (a − b)² = a² − 2ab + b² to find 13².
25. 25.Find the value of x² − y² when x = 11 and y = 9.
26. 26.Use a² − b² = (a + b)(a − b) to find 30² − 27².
27. 27.Use (a + b)(a − b) = a² − b² to find 69 × 51.
28. 28.If a + b = 8 and ab = 7, what is a² + b²?
29. 29.Use (a + b)² = a² + 2ab + b² to find 53².
30. 30.If a + b = 3 and ab = 2, what is a² + b²?
31. 31.Find the value of x² + 2xy + y² when x = 5 and y = 4.
32. 32.Use (a + b)(a − b) = a² − b² to find 81 × 79.
33. 33.Use (a + b)(a − b) = a² − b² to find 21 × 19.
34. 34.Use a² − b² = (a + b)(a − b) to find 42² − 40².
35. 35.Use (a − b)² = a² − 2ab + b² to find 78².
36. 36.Use a² − b² = (a + b)(a − b) to find 45² − 12².
37. 37.Use (a + b)² = a² + 2ab + b² to find 106².
38. 38.Use a² − b² = (a + b)(a − b) to find 90² − 49².
39. 39.Use (a + b)² = a² + 2ab + b² to find 97².
40. 40.Use a² − b² = (a + b)(a − b) to find 80² − 62².

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