Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 995 · 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.Find the value of x² − y² when x = 11 and y = 7.
2. 2.Find the value of x² + 2xy + y² when x = 7 and y = 6.
3. 3.Find the value of x² − y² when x = 14 and y = 12.
4. 4.Use (a + b)(a − b) = a² − b² to find 72 × 68.
5. 5.Use (a + b)² = a² + 2ab + b² to find 74².
6. 6.Use (a − b)² = a² − 2ab + b² to find 84².
7. 7.If a − b = 4 and ab = 12, what is a² + b²?
8. 8.Use (a + b)(a − b) = a² − b² to find 22 × 18.
9. 9.Use (a + b)(a − b) = a² − b² to find 33 × 27.
10. 10.Use (a + b)² = a² + 2ab + b² to find 27².
11. 11.Use a² − b² = (a + b)(a − b) to find 82² − 28².
12. 12.Use a² − b² = (a + b)(a − b) to find 54² − 32².
13. 13.Use a² − b² = (a + b)(a − b) to find 26² − 4².
14. 14.Use a² − b² = (a + b)(a − b) to find 82² − 12².
15. 15.If a − b = 7 and ab = 8, what is a² + b²?
16. 16.Use (a − b)² = a² − 2ab + b² to find 17².
17. 17.If a + b = 15 and ab = 54, what is a² + b²?
18. 18.Use (a + b)(a − b) = a² − b² to find 23 × 17.
19. 19.Use (a + b)(a − b) = a² − b² to find 75 × 65.
20. 20.Use (a − b)² = a² − 2ab + b² to find 13².
21. 21.If a + b = 3 and ab = 2, what is a² + b²?
22. 22.Use (a + b)(a − b) = a² − b² to find 107 × 93.
23. 23.Use (a + b)² = a² + 2ab + b² to find 92².
24. 24.Use (a − b)² = a² − 2ab + b² to find 38².
25. 25.Use (a + b)(a − b) = a² − b² to find 43 × 37.
26. 26.Find the value of x² − y² when x = 13 and y = 9.
27. 27.Find the value of x² − 2xy + y² when x = 7 and y = 3.
28. 28.Use (a − b)² = a² − 2ab + b² to find 87².
29. 29.Use (a + b)(a − b) = a² − b² to find 21 × 19.
30. 30.Use (a − b)² = a² − 2ab + b² to find 81².
31. 31.Use (a + b)(a − b) = a² − b² to find 57 × 43.
32. 32.Use (a + b)(a − b) = a² − b² to find 55 × 45.
33. 33.Use a² − b² = (a + b)(a − b) to find 30² − 25².
34. 34.Use (a + b)² = a² + 2ab + b² to find 69².
35. 35.Use (a − b)² = a² − 2ab + b² to find 51².
36. 36.Use (a − b)² = a² − 2ab + b² to find 64².
37. 37.Find the value of x² − y² when x = 10 and y = 3.
38. 38.Use (a + b)² = a² + 2ab + b² to find 31².
39. 39.Find the value of x² − 2xy + y² when x = 15 and y = 13.
40. 40.Use (a − b)² = a² − 2ab + b² to find 33².

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