Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 228 · 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 21².
2. 2.Find the value of x² + 2xy + y² when x = 4 and y = 2.
3. 3.Find the value of x² + 2xy + y² when x = 14 and y = 4.
4. 4.Use (a + b)² = a² + 2ab + b² to find 47².
5. 5.Use (a + b)² = a² + 2ab + b² to find 61².
6. 6.Use a² − b² = (a + b)(a − b) to find 64² − 45².
7. 7.Use (a + b)² = a² + 2ab + b² to find 104².
8. 8.Use (a + b)² = a² + 2ab + b² to find 105².
9. 9.Find the value of x² + 2xy + y² when x = 6 and y = 1.
10. 10.Use a² − b² = (a + b)(a − b) to find 31² − 3².
11. 11.Use a² − b² = (a + b)(a − b) to find 67² − 52².
12. 12.Use (a + b)² = a² + 2ab + b² to find 18².
13. 13.Use a² − b² = (a + b)(a − b) to find 49² − 24².
14. 14.Use (a − b)² = a² − 2ab + b² to find 58².
15. 15.Use (a + b)(a − b) = a² − b² to find 37 × 23.
16. 16.Use a² − b² = (a + b)(a − b) to find 49² − 15².
17. 17.Use (a − b)² = a² − 2ab + b² to find 55².
18. 18.Use (a + b)² = a² + 2ab + b² to find 64².
19. 19.Use (a + b)² = a² + 2ab + b² to find 51².
20. 20.Use (a + b)(a − b) = a² − b² to find 86 × 74.
21. 21.If a − b = 1 and ab = 72, what is a² + b²?
22. 22.If a − b = 1 and ab = 6, what is a² + b²?
23. 23.If a + b = 8 and ab = 7, what is a² + b²?
24. 24.Use a² − b² = (a + b)(a − b) to find 72² − 14².
25. 25.Use (a + b)² = a² + 2ab + b² to find 28².
26. 26.Use a² − b² = (a + b)(a − b) to find 85² − 40².
27. 27.Use (a + b)² = a² + 2ab + b² to find 29².
28. 28.If a − b = 1 and ab = 20, what is a² + b²?
29. 29.If a + b = 10 and ab = 24, what is a² + b²?
30. 30.Use (a + b)(a − b) = a² − b² to find 31 × 29.
31. 31.Use (a + b)² = a² + 2ab + b² to find 108².
32. 32.If a + b = 19 and ab = 88, what is a² + b²?
33. 33.Use (a + b)(a − b) = a² − b² to find 85 × 75.
34. 34.If a − b = 7 and ab = 60, what is a² + b²?
35. 35.Use (a + b)(a − b) = a² − b² to find 22 × 18.
36. 36.Use (a − b)² = a² − 2ab + b² to find 43².
37. 37.Use (a + b)² = a² + 2ab + b² to find 31².
38. 38.If a − b = 6 and ab = 16, what is a² + b²?
39. 39.Use a² − b² = (a + b)(a − b) to find 68² − 28².
40. 40.Use (a + b)² = a² + 2ab + b² to find 58².

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