Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 913 · 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.Use (a + b)² = a² + 2ab + b² to find 48².
3. 3.Use (a − b)² = a² − 2ab + b² to find 22².
4. 4.If a − b = 5 and ab = 6, what is a² + b²?
5. 5.Use (a + b)² = a² + 2ab + b² to find 37².
6. 6.Use (a − b)² = a² − 2ab + b² to find 63².
7. 7.Use a² − b² = (a + b)(a − b) to find 90² − 79².
8. 8.Use (a + b)² = a² + 2ab + b² to find 13².
9. 9.Use (a + b)² = a² + 2ab + b² to find 21².
10. 10.Use (a + b)(a − b) = a² − b² to find 85 × 75.
11. 11.Use (a + b)² = a² + 2ab + b² to find 98².
12. 12.Use a² − b² = (a + b)(a − b) to find 93² − 19².
13. 13.If a + b = 17 and ab = 60, what is a² + b²?
14. 14.If a − b = 2 and ab = 24, what is a² + b²?
15. 15.Use (a + b)(a − b) = a² − b² to find 93 × 87.
16. 16.Use (a + b)² = a² + 2ab + b² to find 96².
17. 17.Use (a + b)(a − b) = a² − b² to find 23 × 17.
18. 18.Use (a − b)² = a² − 2ab + b² to find 36².
19. 19.Use a² − b² = (a + b)(a − b) to find 41² − 9².
20. 20.Use (a − b)² = a² − 2ab + b² to find 12².
21. 21.Find the value of x² − y² when x = 10 and y = 8.
22. 22.Use a² − b² = (a + b)(a − b) to find 23² − 10².
23. 23.Use (a + b)² = a² + 2ab + b² to find 46².
24. 24.If a + b = 12 and ab = 20, what is a² + b²?
25. 25.Use (a + b)² = a² + 2ab + b² to find 65².
26. 26.Use (a + b)(a − b) = a² − b² to find 24 × 16.
27. 27.If a + b = 4 and ab = 3, what is a² + b²?
28. 28.Use a² − b² = (a + b)(a − b) to find 69² − 9².
29. 29.Find the value of x² + 2xy + y² when x = 10 and y = 9.
30. 30.Use (a − b)² = a² − 2ab + b² to find 59².
31. 31.Use (a + b)(a − b) = a² − b² to find 74 × 66.
32. 32.Use a² − b² = (a + b)(a − b) to find 44² − 15².
33. 33.Use a² − b² = (a + b)(a − b) to find 75² − 48².
34. 34.Use a² − b² = (a + b)(a − b) to find 84² − 57².
35. 35.Use (a + b)(a − b) = a² − b² to find 78 × 62.
36. 36.Use a² − b² = (a + b)(a − b) to find 83² − 1².
37. 37.Use (a + b)(a − b) = a² − b² to find 39 × 21.
38. 38.Use a² − b² = (a + b)(a − b) to find 30² − 16².
39. 39.If a + b = 8 and ab = 12, what is a² + b²?
40. 40.If a − b = 1 and ab = 132, what is a² + b²?

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