Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 173 · 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)(a − b) = a² − b² to find 97 × 83.
2. 2.Use a² − b² = (a + b)(a − b) to find 54² − 35².
3. 3.Use (a − b)² = a² − 2ab + b² to find 27².
4. 4.Use (a − b)² = a² − 2ab + b² to find 25².
5. 5.Use (a + b)² = a² + 2ab + b² to find 61².
6. 6.Use (a − b)² = a² − 2ab + b² to find 19².
7. 7.Use (a + b)(a − b) = a² − b² to find 45 × 35.
8. 8.If a − b = 1 and ab = 90, what is a² + b²?
9. 9.Use (a + b)² = a² + 2ab + b² to find 32².
10. 10.Use (a + b)² = a² + 2ab + b² to find 36².
11. 11.Use a² − b² = (a + b)(a − b) to find 97² − 42².
12. 12.If a + b = 5 and ab = 6, what is a² + b²?
13. 13.Find the value of x² − 2xy + y² when x = 10 and y = 1.
14. 14.Find the value of x² − 2xy + y² when x = 10 and y = 3.
15. 15.If a − b = 4 and ab = 45, what is a² + b²?
16. 16.Use (a + b)² = a² + 2ab + b² to find 42².
17. 17.Find the value of x² − y² when x = 11 and y = 10.
18. 18.If a + b = 6 and ab = 8, what is a² + b²?
19. 19.Use (a − b)² = a² − 2ab + b² to find 85².
20. 20.Use a² − b² = (a + b)(a − b) to find 29² − 5².
21. 21.Use (a + b)² = a² + 2ab + b² to find 92².
22. 22.If a − b = 4 and ab = 21, what is a² + b²?
23. 23.Use (a − b)² = a² − 2ab + b² to find 98².
24. 24.If a − b = 1 and ab = 12, what is a² + b²?
25. 25.Find the value of x² − y² when x = 12 and y = 4.
26. 26.Use (a + b)(a − b) = a² − b² to find 75 × 65.
27. 27.Find the value of x² + 2xy + y² when x = 6 and y = 1.
28. 28.Use a² − b² = (a + b)(a − b) to find 25² − 15².
29. 29.If a − b = 8 and ab = 9, what is a² + b²?
30. 30.Use (a − b)² = a² − 2ab + b² to find 42².
31. 31.Use a² − b² = (a + b)(a − b) to find 45² − 30².
32. 32.Use (a − b)² = a² − 2ab + b² to find 65².
33. 33.Use (a + b)² = a² + 2ab + b² to find 102².
34. 34.Use (a − b)² = a² − 2ab + b² to find 67².
35. 35.Use a² − b² = (a + b)(a − b) to find 99² − 52².
36. 36.Find the value of x² + 2xy + y² when x = 4 and y = 3.
37. 37.Use a² − b² = (a + b)(a − b) to find 64² − 57².
38. 38.Use (a − b)² = a² − 2ab + b² to find 17².
39. 39.Use (a − b)² = a² − 2ab + b² to find 28².
40. 40.Use (a − b)² = a² − 2ab + b² to find 69².

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