Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 726 · 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 94².
2. 2.Use a² − b² = (a + b)(a − b) to find 50² − 40².
3. 3.Find the value of x² + 2xy + y² when x = 7 and y = 1.
4. 4.Find the value of x² − y² when x = 8 and y = 3.
5. 5.Use (a − b)² = a² − 2ab + b² to find 29².
6. 6.Use (a − b)² = a² − 2ab + b² to find 71².
7. 7.Use (a − b)² = a² − 2ab + b² to find 32².
8. 8.Use (a − b)² = a² − 2ab + b² to find 53².
9. 9.Use (a + b)² = a² + 2ab + b² to find 22².
10. 10.Use a² − b² = (a + b)(a − b) to find 39² − 23².
11. 11.Use (a + b)(a − b) = a² − b² to find 63 × 57.
12. 12.Use (a − b)² = a² − 2ab + b² to find 34².
13. 13.If a + b = 16 and ab = 63, what is a² + b²?
14. 14.Use (a + b)(a − b) = a² − b² to find 104 × 96.
15. 15.Find the value of x² − 2xy + y² when x = 4 and y = 2.
16. 16.Use (a − b)² = a² − 2ab + b² to find 31².
17. 17.Use (a − b)² = a² − 2ab + b² to find 36².
18. 18.Use (a + b)(a − b) = a² − b² to find 99 × 81.
19. 19.Use (a + b)² = a² + 2ab + b² to find 17².
20. 20.Find the value of x² − 2xy + y² when x = 6 and y = 1.
21. 21.Find the value of x² − y² when x = 11 and y = 10.
22. 22.Use a² − b² = (a + b)(a − b) to find 31² − 14².
23. 23.Use (a − b)² = a² − 2ab + b² to find 26².
24. 24.If a − b = 7 and ab = 8, what is a² + b²?
25. 25.Use (a − b)² = a² − 2ab + b² to find 18².
26. 26.If a − b = 5 and ab = 24, what is a² + b²?
27. 27.Use (a − b)² = a² − 2ab + b² to find 74².
28. 28.If a + b = 3 and ab = 2, what is a² + b²?
29. 29.Use (a + b)(a − b) = a² − b² to find 81 × 79.
30. 30.Use (a + b)(a − b) = a² − b² to find 22 × 18.
31. 31.If a − b = 3 and ab = 70, what is a² + b²?
32. 32.Use a² − b² = (a + b)(a − b) to find 91² − 27².
33. 33.Use (a − b)² = a² − 2ab + b² to find 82².
34. 34.Use (a + b)(a − b) = a² − b² to find 76 × 64.
35. 35.Use a² − b² = (a + b)(a − b) to find 28² − 20².
36. 36.Use (a − b)² = a² − 2ab + b² to find 24².
37. 37.Use (a + b)(a − b) = a² − b² to find 57 × 43.
38. 38.Use (a + b)² = a² + 2ab + b² to find 61².
39. 39.Use (a + b)² = a² + 2ab + b² to find 13².
40. 40.If a − b = 2 and ab = 24, what is a² + b²?

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