Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 535 · 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 47².
2. 2.If a + b = 4 and ab = 3, what is a² + b²?
3. 3.Find the value of x² − 2xy + y² when x = 8 and y = 5.
4. 4.Use (a + b)(a − b) = a² − b² to find 28 × 12.
5. 5.Use (a + b)(a − b) = a² − b² to find 75 × 65.
6. 6.Use (a + b)² = a² + 2ab + b² to find 99².
7. 7.Use (a + b)(a − b) = a² − b² to find 24 × 16.
8. 8.Use (a + b)² = a² + 2ab + b² to find 64².
9. 9.Use (a + b)² = a² + 2ab + b² to find 53².
10. 10.Use (a + b)² = a² + 2ab + b² to find 83².
11. 11.Use (a + b)² = a² + 2ab + b² to find 102².
12. 12.Use (a + b)² = a² + 2ab + b² to find 108².
13. 13.Use a² − b² = (a + b)(a − b) to find 72² − 18².
14. 14.Use (a − b)² = a² − 2ab + b² to find 25².
15. 15.Use (a + b)² = a² + 2ab + b² to find 85².
16. 16.Use (a + b)² = a² + 2ab + b² to find 78².
17. 17.Use a² − b² = (a + b)(a − b) to find 21² − 16².
18. 18.If a − b = 9 and ab = 22, what is a² + b²?
19. 19.Use (a + b)² = a² + 2ab + b² to find 57².
20. 20.Use (a − b)² = a² − 2ab + b² to find 87².
21. 21.Use (a − b)² = a² − 2ab + b² to find 37².
22. 22.If a − b = 4 and ab = 5, what is a² + b²?
23. 23.If a + b = 9 and ab = 18, what is a² + b²?
24. 24.Use (a − b)² = a² − 2ab + b² to find 22².
25. 25.Find the value of x² + 2xy + y² when x = 12 and y = 5.
26. 26.Use (a − b)² = a² − 2ab + b² to find 82².
27. 27.Use (a + b)² = a² + 2ab + b² to find 26².
28. 28.Use (a + b)(a − b) = a² − b² to find 81 × 79.
29. 29.Use (a + b)² = a² + 2ab + b² to find 23².
30. 30.Use (a + b)² = a² + 2ab + b² to find 49².
31. 31.If a + b = 19 and ab = 88, what is a² + b²?
32. 32.Use a² − b² = (a + b)(a − b) to find 80² − 11².
33. 33.Use (a + b)² = a² + 2ab + b² to find 21².
34. 34.Use (a − b)² = a² − 2ab + b² to find 38².
35. 35.If a − b = 3 and ab = 28, what is a² + b²?
36. 36.Find the value of x² − 2xy + y² when x = 3 and y = 2.
37. 37.Use (a + b)(a − b) = a² − b² to find 45 × 35.
38. 38.Use (a − b)² = a² − 2ab + b² to find 85².
39. 39.Use (a + b)(a − b) = a² − b² to find 43 × 37.
40. 40.Use a² − b² = (a + b)(a − b) to find 40² − 22².

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