Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 834 · 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 42 × 38.
2. 2.Use a² − b² = (a + b)(a − b) to find 46² − 38².
3. 3.Find the value of x² − y² when x = 15 and y = 13.
4. 4.Find the value of x² + 2xy + y² when x = 5 and y = 4.
5. 5.Find the value of x² + 2xy + y² when x = 15 and y = 5.
6. 6.Find the value of x² + 2xy + y² when x = 10 and y = 4.
7. 7.Use a² − b² = (a + b)(a − b) to find 85² − 76².
8. 8.Use (a + b)(a − b) = a² − b² to find 54 × 46.
9. 9.Use (a + b)(a − b) = a² − b² to find 97 × 83.
10. 10.Use a² − b² = (a + b)(a − b) to find 30² − 23².
11. 11.Use (a + b)(a − b) = a² − b² to find 104 × 96.
12. 12.If a + b = 9 and ab = 20, what is a² + b²?
13. 13.Use a² − b² = (a + b)(a − b) to find 60² − 29².
14. 14.Find the value of x² − 2xy + y² when x = 5 and y = 2.
15. 15.Find the value of x² + 2xy + y² when x = 9 and y = 2.
16. 16.Find the value of x² − 2xy + y² when x = 5 and y = 1.
17. 17.If a − b = 1 and ab = 2, what is a² + b²?
18. 18.Use (a + b)(a − b) = a² − b² to find 36 × 24.
19. 19.Use (a − b)² = a² − 2ab + b² to find 82².
20. 20.Use a² − b² = (a + b)(a − b) to find 30² − 18².
21. 21.Use (a − b)² = a² − 2ab + b² to find 93².
22. 22.If a + b = 11 and ab = 10, what is a² + b²?
23. 23.Find the value of x² − y² when x = 11 and y = 6.
24. 24.Use (a + b)(a − b) = a² − b² to find 76 × 64.
25. 25.Use (a + b)² = a² + 2ab + b² to find 13².
26. 26.If a + b = 8 and ab = 15, what is a² + b²?
27. 27.Use (a + b)(a − b) = a² − b² to find 33 × 27.
28. 28.Use (a + b)(a − b) = a² − b² to find 31 × 29.
29. 29.Use (a + b)² = a² + 2ab + b² to find 67².
30. 30.Use (a + b)² = a² + 2ab + b² to find 75².
31. 31.Use (a + b)(a − b) = a² − b² to find 24 × 16.
32. 32.Use (a − b)² = a² − 2ab + b² to find 69².
33. 33.Use a² − b² = (a + b)(a − b) to find 57² − 9².
34. 34.Use (a − b)² = a² − 2ab + b² to find 16².
35. 35.Use (a + b)² = a² + 2ab + b² to find 32².
36. 36.Use (a + b)² = a² + 2ab + b² to find 22².
37. 37.Use a² − b² = (a + b)(a − b) to find 51² − 13².
38. 38.Find the value of x² + 2xy + y² when x = 11 and y = 1.
39. 39.Use (a − b)² = a² − 2ab + b² to find 84².
40. 40.Use (a + b)² = a² + 2ab + b² to find 97².

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