Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 944 · 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 = 16 and ab = 63, what is a² + b²?
2. 2.Use (a + b)(a − b) = a² − b² to find 31 × 29.
3. 3.If a + b = 3 and ab = 2, what is a² + b²?
4. 4.Use a² − b² = (a + b)(a − b) to find 50² − 3².
5. 5.Use (a + b)² = a² + 2ab + b² to find 14².
6. 6.Use (a + b)² = a² + 2ab + b² to find 49².
7. 7.Use (a − b)² = a² − 2ab + b² to find 59².
8. 8.Use (a + b)² = a² + 2ab + b² to find 82².
9. 9.Find the value of x² + 2xy + y² when x = 10 and y = 7.
10. 10.If a + b = 10 and ab = 21, what is a² + b²?
11. 11.Find the value of x² − y² when x = 5 and y = 4.
12. 12.Use a² − b² = (a + b)(a − b) to find 20² − 11².
13. 13.Find the value of x² + 2xy + y² when x = 4 and y = 3.
14. 14.Find the value of x² − y² when x = 4 and y = 3.
15. 15.Use (a − b)² = a² − 2ab + b² to find 48².
16. 16.If a − b = 2 and ab = 24, what is a² + b²?
17. 17.If a + b = 14 and ab = 24, what is a² + b²?
18. 18.Find the value of x² − y² when x = 6 and y = 2.
19. 19.Use (a − b)² = a² − 2ab + b² to find 33².
20. 20.Use (a − b)² = a² − 2ab + b² to find 69².
21. 21.Use a² − b² = (a + b)(a − b) to find 23² − 15².
22. 22.Use a² − b² = (a + b)(a − b) to find 68² − 34².
23. 23.Use (a − b)² = a² − 2ab + b² to find 45².
24. 24.If a + b = 7 and ab = 10, what is a² + b²?
25. 25.Use a² − b² = (a + b)(a − b) to find 50² − 44².
26. 26.Use a² − b² = (a + b)(a − b) to find 94² − 74².
27. 27.Use (a − b)² = a² − 2ab + b² to find 46².
28. 28.Use (a − b)² = a² − 2ab + b² to find 53².
29. 29.Find the value of x² − y² when x = 3 and y = 1.
30. 30.Use (a + b)(a − b) = a² − b² to find 43 × 37.
31. 31.Find the value of x² − 2xy + y² when x = 13 and y = 9.
32. 32.Use (a + b)² = a² + 2ab + b² to find 16².
33. 33.Use (a + b)(a − b) = a² − b² to find 47 × 33.
34. 34.Use a² − b² = (a + b)(a − b) to find 80² − 25².
35. 35.If a + b = 8 and ab = 12, what is a² + b²?
36. 36.If a + b = 7 and ab = 12, what is a² + b²?
37. 37.Use (a + b)² = a² + 2ab + b² to find 63².
38. 38.Find the value of x² − 2xy + y² when x = 13 and y = 8.
39. 39.Use (a + b)(a − b) = a² − b² to find 82 × 78.
40. 40.Use (a + b)(a − b) = a² − b² to find 66 × 54.

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