Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 470 · 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 84².
2. 2.If a − b = 2 and ab = 3, what is a² + b²?
3. 3.Use (a + b)(a − b) = a² − b² to find 67 × 53.
4. 4.Use (a − b)² = a² − 2ab + b² to find 48².
5. 5.Use (a + b)(a − b) = a² − b² to find 99 × 81.
6. 6.Use (a + b)² = a² + 2ab + b² to find 92².
7. 7.Use (a + b)² = a² + 2ab + b² to find 22².
8. 8.If a + b = 5 and ab = 6, what is a² + b²?
9. 9.Use (a + b)² = a² + 2ab + b² to find 34².
10. 10.If a + b = 3 and ab = 2, what is a² + b²?
11. 11.Use (a + b)(a − b) = a² − b² to find 45 × 35.
12. 12.Use (a − b)² = a² − 2ab + b² to find 15².
13. 13.Use (a + b)(a − b) = a² − b² to find 21 × 19.
14. 14.Use a² − b² = (a + b)(a − b) to find 40² − 11².
15. 15.If a − b = 7 and ab = 8, what is a² + b²?
16. 16.Use a² − b² = (a + b)(a − b) to find 37² − 31².
17. 17.Use (a − b)² = a² − 2ab + b² to find 17².
18. 18.Use (a − b)² = a² − 2ab + b² to find 98².
19. 19.Use a² − b² = (a + b)(a − b) to find 55² − 26².
20. 20.If a + b = 14 and ab = 48, what is a² + b²?
21. 21.Use (a + b)² = a² + 2ab + b² to find 105².
22. 22.If a − b = 1 and ab = 12, what is a² + b²?
23. 23.If a − b = 4 and ab = 32, what is a² + b²?
24. 24.Use (a + b)(a − b) = a² − b² to find 31 × 29.
25. 25.Find the value of x² − 2xy + y² when x = 11 and y = 9.
26. 26.Use (a − b)² = a² − 2ab + b² to find 62².
27. 27.Find the value of x² − 2xy + y² when x = 8 and y = 2.
28. 28.If a + b = 21 and ab = 108, what is a² + b²?
29. 29.If a − b = 6 and ab = 7, what is a² + b²?
30. 30.Use a² − b² = (a + b)(a − b) to find 79² − 55².
31. 31.Use (a − b)² = a² − 2ab + b² to find 94².
32. 32.If a + b = 4 and ab = 3, what is a² + b²?
33. 33.Use (a + b)² = a² + 2ab + b² to find 21².
34. 34.Use (a + b)² = a² + 2ab + b² to find 36².
35. 35.Use (a + b)(a − b) = a² − b² to find 29 × 11.
36. 36.If a + b = 14 and ab = 45, what is a² + b²?
37. 37.If a − b = 3 and ab = 40, what is a² + b²?
38. 38.Use (a + b)² = a² + 2ab + b² to find 12².
39. 39.Use (a + b)² = a² + 2ab + b² to find 57².
40. 40.If a − b = 3 and ab = 28, what is a² + b²?

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