Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 647 · 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 = 5 and ab = 6, what is a² + b²?
2. 2.If a + b = 22 and ab = 120, what is a² + b²?
3. 3.Use (a − b)² = a² − 2ab + b² to find 32².
4. 4.If a + b = 15 and ab = 36, what is a² + b²?
5. 5.Find the value of x² − 2xy + y² when x = 3 and y = 2.
6. 6.Use (a − b)² = a² − 2ab + b² to find 68².
7. 7.If a − b = 10 and ab = 11, what is a² + b²?
8. 8.Use (a − b)² = a² − 2ab + b² to find 27².
9. 9.Use a² − b² = (a + b)(a − b) to find 98² − 3².
10. 10.Use (a − b)² = a² − 2ab + b² to find 56².
11. 11.Use (a − b)² = a² − 2ab + b² to find 62².
12. 12.If a + b = 10 and ab = 16, what is a² + b²?
13. 13.If a + b = 15 and ab = 50, what is a² + b²?
14. 14.Find the value of x² − y² when x = 11 and y = 1.
15. 15.Use a² − b² = (a + b)(a − b) to find 47² − 12².
16. 16.Use (a + b)² = a² + 2ab + b² to find 21².
17. 17.Find the value of x² − y² when x = 6 and y = 1.
18. 18.Use (a + b)² = a² + 2ab + b² to find 39².
19. 19.Use (a + b)² = a² + 2ab + b² to find 13².
20. 20.If a + b = 18 and ab = 72, what is a² + b²?
21. 21.If a + b = 8 and ab = 7, what is a² + b²?
22. 22.Use (a − b)² = a² − 2ab + b² to find 21².
23. 23.Use (a + b)² = a² + 2ab + b² to find 61².
24. 24.Find the value of x² − y² when x = 11 and y = 10.
25. 25.Use (a − b)² = a² − 2ab + b² to find 83².
26. 26.Use a² − b² = (a + b)(a − b) to find 71² − 52².
27. 27.If a + b = 8 and ab = 12, what is a² + b²?
28. 28.Use a² − b² = (a + b)(a − b) to find 53² − 33².
29. 29.Find the value of x² − y² when x = 11 and y = 6.
30. 30.Use (a − b)² = a² − 2ab + b² to find 14².
31. 31.If a − b = 2 and ab = 3, what is a² + b²?
32. 32.Use (a + b)(a − b) = a² − b² to find 63 × 57.
33. 33.Use (a + b)(a − b) = a² − b² to find 74 × 66.
34. 34.If a + b = 20 and ab = 96, what is a² + b²?
35. 35.If a − b = 3 and ab = 88, what is a² + b²?
36. 36.Find the value of x² − y² when x = 10 and y = 6.
37. 37.Find the value of x² − 2xy + y² when x = 9 and y = 3.
38. 38.Use (a + b)² = a² + 2ab + b² to find 55².
39. 39.Use (a + b)(a − b) = a² − b² to find 94 × 86.
40. 40.If a + b = 10 and ab = 9, what is a² + b²?

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