Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 77 · 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.Find the value of x² + 2xy + y² when x = 10 and y = 2.
3. 3.Use (a + b)(a − b) = a² − b² to find 54 × 46.
4. 4.Find the value of x² − 2xy + y² when x = 10 and y = 4.
5. 5.Use (a + b)(a − b) = a² − b² to find 31 × 29.
6. 6.Use a² − b² = (a + b)(a − b) to find 45² − 4².
7. 7.Use (a + b)² = a² + 2ab + b² to find 26².
8. 8.Find the value of x² − y² when x = 4 and y = 1.
9. 9.If a + b = 13 and ab = 40, what is a² + b²?
10. 10.Use (a + b)² = a² + 2ab + b² to find 81².
11. 11.Use (a + b)(a − b) = a² − b² to find 102 × 98.
12. 12.Find the value of x² − y² when x = 3 and y = 1.
13. 13.If a − b = 1 and ab = 56, what is a² + b²?
14. 14.If a + b = 3 and ab = 2, what is a² + b²?
15. 15.Use a² − b² = (a + b)(a − b) to find 48² − 38².
16. 16.Find the value of x² + 2xy + y² when x = 7 and y = 3.
17. 17.Use a² − b² = (a + b)(a − b) to find 67² − 14².
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 16².
20. 20.Use (a − b)² = a² − 2ab + b² to find 77².
21. 21.Find the value of x² − 2xy + y² when x = 4 and y = 2.
22. 22.Find the value of x² + 2xy + y² when x = 8 and y = 2.
23. 23.Use (a − b)² = a² − 2ab + b² to find 46².
24. 24.Use (a + b)² = a² + 2ab + b² to find 15².
25. 25.Use (a + b)² = a² + 2ab + b² to find 94².
26. 26.Use (a + b)(a − b) = a² − b² to find 91 × 89.
27. 27.Use (a − b)² = a² − 2ab + b² to find 16².
28. 28.Find the value of x² + 2xy + y² when x = 6 and y = 5.
29. 29.Use (a + b)² = a² + 2ab + b² to find 92².
30. 30.Use a² − b² = (a + b)(a − b) to find 23² − 8².
31. 31.Use a² − b² = (a + b)(a − b) to find 39² − 17².
32. 32.Use a² − b² = (a + b)(a − b) to find 26² − 17².
33. 33.Use a² − b² = (a + b)(a − b) to find 43² − 6².
34. 34.If a − b = 3 and ab = 40, what is a² + b²?
35. 35.If a + b = 11 and ab = 10, what is a² + b²?
36. 36.Use (a + b)² = a² + 2ab + b² to find 47².
37. 37.If a − b = 1 and ab = 2, what is a² + b²?
38. 38.Use a² − b² = (a + b)(a − b) to find 34² − 29².
39. 39.If a + b = 19 and ab = 90, what is a² + b²?
40. 40.If a + b = 9 and ab = 18, what is a² + b²?

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