Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 570 · 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 34² − 10².
2. 2.Use (a − b)² = a² − 2ab + b² to find 52².
3. 3.Use a² − b² = (a + b)(a − b) to find 92² − 21².
4. 4.Use (a − b)² = a² − 2ab + b² to find 88².
5. 5.Find the value of x² + 2xy + y² when x = 4 and y = 2.
6. 6.Use (a − b)² = a² − 2ab + b² to find 25².
7. 7.If a + b = 5 and ab = 6, what is a² + b²?
8. 8.Use (a + b)² = a² + 2ab + b² to find 19².
9. 9.Use (a + b)(a − b) = a² − b² to find 38 × 22.
10. 10.Use (a − b)² = a² − 2ab + b² to find 21².
11. 11.If a + b = 20 and ab = 99, what is a² + b²?
12. 12.Use (a + b)² = a² + 2ab + b² to find 69².
13. 13.Find the value of x² − y² when x = 3 and y = 2.
14. 14.If a + b = 14 and ab = 40, what is a² + b²?
15. 15.Find the value of x² − y² when x = 15 and y = 2.
16. 16.If a − b = 6 and ab = 40, what is a² + b²?
17. 17.Use (a + b)² = a² + 2ab + b² to find 21².
18. 18.Find the value of x² + 2xy + y² when x = 3 and y = 1.
19. 19.Use (a + b)² = a² + 2ab + b² to find 77².
20. 20.Use (a + b)(a − b) = a² − b² to find 33 × 27.
21. 21.Use (a − b)² = a² − 2ab + b² to find 22².
22. 22.If a + b = 4 and ab = 3, what is a² + b²?
23. 23.Use a² − b² = (a + b)(a − b) to find 67² − 2².
24. 24.Use a² − b² = (a + b)(a − b) to find 60² − 17².
25. 25.Use (a + b)(a − b) = a² − b² to find 106 × 94.
26. 26.Use (a + b)(a − b) = a² − b² to find 37 × 23.
27. 27.Use (a + b)(a − b) = a² − b² to find 93 × 87.
28. 28.Use (a + b)(a − b) = a² − b² to find 98 × 82.
29. 29.If a + b = 7 and ab = 6, what is a² + b²?
30. 30.Use (a − b)² = a² − 2ab + b² to find 17².
31. 31.Use (a + b)(a − b) = a² − b² to find 27 × 13.
32. 32.Use (a + b)² = a² + 2ab + b² to find 32².
33. 33.Use (a + b)² = a² + 2ab + b² to find 96².
34. 34.Find the value of x² − 2xy + y² when x = 4 and y = 2.
35. 35.Use (a + b)² = a² + 2ab + b² to find 63².
36. 36.Find the value of x² − y² when x = 5 and y = 1.
37. 37.Use (a − b)² = a² − 2ab + b² to find 49².
38. 38.Use a² − b² = (a + b)(a − b) to find 93² − 9².
39. 39.If a + b = 14 and ab = 24, what is a² + b²?
40. 40.Use (a + b)(a − b) = a² − b² to find 44 × 36.

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