Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 57 · 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.If a − b = 3 and ab = 40, what is a² + b²?
2. 2.Use a² − b² = (a + b)(a − b) to find 36² − 21².
3. 3.If a − b = 1 and ab = 2, what is a² + b²?
4. 4.Use (a + b)(a − b) = a² − b² to find 89 × 71.
5. 5.Use (a + b)² = a² + 2ab + b² to find 109².
6. 6.Use a² − b² = (a + b)(a − b) to find 36² − 32².
7. 7.If a + b = 6 and ab = 5, what is a² + b²?
8. 8.Use (a + b)² = a² + 2ab + b² to find 18².
9. 9.Use (a + b)² = a² + 2ab + b² to find 91².
10. 10.If a + b = 4 and ab = 3, what is a² + b²?
11. 11.Use a² − b² = (a + b)(a − b) to find 42² − 33².
12. 12.Find the value of x² + 2xy + y² when x = 12 and y = 4.
13. 13.Use a² − b² = (a + b)(a − b) to find 63² − 56².
14. 14.If a + b = 3 and ab = 2, what is a² + b²?
15. 15.If a + b = 18 and ab = 80, what is a² + b²?
16. 16.Use (a − b)² = a² − 2ab + b² to find 64².
17. 17.Use (a − b)² = a² − 2ab + b² to find 61².
18. 18.Use (a + b)² = a² + 2ab + b² to find 27².
19. 19.Use (a + b)(a − b) = a² − b² to find 91 × 89.
20. 20.Use (a + b)(a − b) = a² − b² to find 38 × 22.
21. 21.Use a² − b² = (a + b)(a − b) to find 51² − 11².
22. 22.Find the value of x² − y² when x = 4 and y = 1.
23. 23.Use (a + b)² = a² + 2ab + b² to find 22².
24. 24.Use (a + b)(a − b) = a² − b² to find 78 × 62.
25. 25.Find the value of x² − y² when x = 7 and y = 2.
26. 26.Use (a − b)² = a² − 2ab + b² to find 84².
27. 27.Use (a + b)² = a² + 2ab + b² to find 34².
28. 28.Use a² − b² = (a + b)(a − b) to find 36² − 20².
29. 29.Use a² − b² = (a + b)(a − b) to find 50² − 6².
30. 30.Use a² − b² = (a + b)(a − b) to find 87² − 68².
31. 31.Use (a + b)² = a² + 2ab + b² to find 83².
32. 32.Find the value of x² − y² when x = 11 and y = 5.
33. 33.Find the value of x² + 2xy + y² when x = 12 and y = 5.
34. 34.Use (a + b)² = a² + 2ab + b² to find 33².
35. 35.Use (a + b)(a − b) = a² − b² to find 32 × 28.
36. 36.Use (a − b)² = a² − 2ab + b² to find 26².
37. 37.Use a² − b² = (a + b)(a − b) to find 21² − 20².
38. 38.Use (a − b)² = a² − 2ab + b² to find 39².
39. 39.Use (a − b)² = a² − 2ab + b² to find 82².
40. 40.Use a² − b² = (a + b)(a − b) to find 99² − 23².

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