Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 579 · 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 26².
2. 2.Use (a + b)² = a² + 2ab + b² to find 101².
3. 3.Find the value of x² − y² when x = 8 and y = 1.
4. 4.Use a² − b² = (a + b)(a − b) to find 93² − 8².
5. 5.Use (a + b)(a − b) = a² − b² to find 94 × 86.
6. 6.Use (a + b)² = a² + 2ab + b² to find 83².
7. 7.Use (a + b)(a − b) = a² − b² to find 23 × 17.
8. 8.Find the value of x² − y² when x = 13 and y = 3.
9. 9.Use (a − b)² = a² − 2ab + b² to find 19².
10. 10.Use a² − b² = (a + b)(a − b) to find 64² − 52².
11. 11.Use (a + b)² = a² + 2ab + b² to find 13².
12. 12.If a − b = 2 and ab = 35, what is a² + b²?
13. 13.Find the value of x² − y² when x = 4 and y = 2.
14. 14.If a + b = 5 and ab = 6, what is a² + b²?
15. 15.Find the value of x² − 2xy + y² when x = 5 and y = 3.
16. 16.Use a² − b² = (a + b)(a − b) to find 73² − 22².
17. 17.Use a² − b² = (a + b)(a − b) to find 90² − 44².
18. 18.Use (a + b)² = a² + 2ab + b² to find 25².
19. 19.Use (a + b)(a − b) = a² − b² to find 76 × 64.
20. 20.Use (a − b)² = a² − 2ab + b² to find 51².
21. 21.Use (a + b)(a − b) = a² − b² to find 56 × 44.
22. 22.Find the value of x² − 2xy + y² when x = 5 and y = 4.
23. 23.Use (a + b)² = a² + 2ab + b² to find 67².
24. 24.Find the value of x² + 2xy + y² when x = 10 and y = 5.
25. 25.If a + b = 13 and ab = 40, what is a² + b²?
26. 26.Find the value of x² + 2xy + y² when x = 3 and y = 2.
27. 27.If a − b = 9 and ab = 10, what is a² + b²?
28. 28.Use a² − b² = (a + b)(a − b) to find 71² − 60².
29. 29.Use a² − b² = (a + b)(a − b) to find 30² − 24².
30. 30.Use a² − b² = (a + b)(a − b) to find 91² − 80².
31. 31.Use (a − b)² = a² − 2ab + b² to find 93².
32. 32.If a − b = 3 and ab = 28, what is a² + b²?
33. 33.Use a² − b² = (a + b)(a − b) to find 36² − 8².
34. 34.If a + b = 9 and ab = 14, what is a² + b²?
35. 35.Find the value of x² − 2xy + y² when x = 12 and y = 7.
36. 36.If a − b = 7 and ab = 30, what is a² + b²?
37. 37.Find the value of x² + 2xy + y² when x = 13 and y = 2.
38. 38.Use a² − b² = (a + b)(a − b) to find 33² − 17².
39. 39.Use (a − b)² = a² − 2ab + b² to find 72².
40. 40.Find the value of x² + 2xy + y² when x = 15 and y = 2.

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