Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 471 · 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 99².
2. 2.Use (a + b)² = a² + 2ab + b² to find 57².
3. 3.Use (a + b)² = a² + 2ab + b² to find 67².
4. 4.If a + b = 7 and ab = 12, what is a² + b²?
5. 5.If a − b = 2 and ab = 15, what is a² + b²?
6. 6.Use a² − b² = (a + b)(a − b) to find 38² − 9².
7. 7.Find the value of x² − 2xy + y² when x = 14 and y = 9.
8. 8.Use (a + b)(a − b) = a² − b² to find 26 × 14.
9. 9.Find the value of x² − 2xy + y² when x = 8 and y = 3.
10. 10.Find the value of x² − y² when x = 3 and y = 2.
11. 11.If a + b = 16 and ab = 63, what is a² + b²?
12. 12.Use (a + b)(a − b) = a² − b² to find 84 × 76.
13. 13.Use a² − b² = (a + b)(a − b) to find 97² − 11².
14. 14.Use (a − b)² = a² − 2ab + b² to find 94².
15. 15.Use a² − b² = (a + b)(a − b) to find 68² − 2².
16. 16.Use (a + b)(a − b) = a² − b² to find 77 × 63.
17. 17.Use (a + b)(a − b) = a² − b² to find 45 × 35.
18. 18.Use (a + b)(a − b) = a² − b² to find 68 × 52.
19. 19.Find the value of x² − y² when x = 14 and y = 1.
20. 20.If a + b = 19 and ab = 88, what is a² + b²?
21. 21.Find the value of x² + 2xy + y² when x = 9 and y = 4.
22. 22.Use (a + b)² = a² + 2ab + b² to find 83².
23. 23.If a − b = 5 and ab = 36, what is a² + b²?
24. 24.Use (a − b)² = a² − 2ab + b² to find 19².
25. 25.If a − b = 5 and ab = 24, what is a² + b²?
26. 26.Use (a + b)² = a² + 2ab + b² to find 76².
27. 27.Use (a + b)² = a² + 2ab + b² to find 43².
28. 28.Use (a + b)² = a² + 2ab + b² to find 14².
29. 29.Find the value of x² + 2xy + y² when x = 6 and y = 4.
30. 30.Use a² − b² = (a + b)(a − b) to find 85² − 6².
31. 31.Use (a − b)² = a² − 2ab + b² to find 69².
32. 32.Use (a + b)(a − b) = a² − b² to find 44 × 36.
33. 33.Use a² − b² = (a + b)(a − b) to find 24² − 6².
34. 34.Use (a − b)² = a² − 2ab + b² to find 64².
35. 35.If a + b = 8 and ab = 15, what is a² + b²?
36. 36.Use (a + b)² = a² + 2ab + b² to find 15².
37. 37.Use (a − b)² = a² − 2ab + b² to find 17².
38. 38.Use a² − b² = (a + b)(a − b) to find 95² − 21².
39. 39.If a − b = 1 and ab = 2, what is a² + b²?
40. 40.Use a² − b² = (a + b)(a − b) to find 88² − 70².

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