Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 525 · 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 23 × 17.
2. 2.Use a² − b² = (a + b)(a − b) to find 90² − 12².
3. 3.Use (a − b)² = a² − 2ab + b² to find 28².
4. 4.Use (a + b)(a − b) = a² − b² to find 91 × 89.
5. 5.Use (a + b)² = a² + 2ab + b² to find 64².
6. 6.Use (a − b)² = a² − 2ab + b² to find 42².
7. 7.Use (a + b)(a − b) = a² − b² to find 43 × 37.
8. 8.Use (a − b)² = a² − 2ab + b² to find 54².
9. 9.Use (a − b)² = a² − 2ab + b² to find 38².
10. 10.Use (a − b)² = a² − 2ab + b² to find 19².
11. 11.Find the value of x² − y² when x = 3 and y = 1.
12. 12.If a − b = 1 and ab = 110, what is a² + b²?
13. 13.Use (a + b)² = a² + 2ab + b² to find 76².
14. 14.If a + b = 9 and ab = 14, what is a² + b²?
15. 15.Find the value of x² + 2xy + y² when x = 7 and y = 2.
16. 16.Use a² − b² = (a + b)(a − b) to find 99² − 25².
17. 17.Find the value of x² + 2xy + y² when x = 13 and y = 4.
18. 18.If a + b = 3 and ab = 2, what is a² + b²?
19. 19.If a + b = 6 and ab = 8, what is a² + b²?
20. 20.Use (a + b)² = a² + 2ab + b² to find 56².
21. 21.Use (a + b)(a − b) = a² − b² to find 69 × 51.
22. 22.Use a² − b² = (a + b)(a − b) to find 48² − 23².
23. 23.Use (a + b)(a − b) = a² − b² to find 83 × 77.
24. 24.Find the value of x² − 2xy + y² when x = 6 and y = 1.
25. 25.Find the value of x² − y² when x = 12 and y = 4.
26. 26.Find the value of x² − 2xy + y² when x = 4 and y = 2.
27. 27.If a + b = 11 and ab = 28, what is a² + b²?
28. 28.Use (a + b)² = a² + 2ab + b² to find 51².
29. 29.If a + b = 7 and ab = 6, what is a² + b²?
30. 30.Find the value of x² − 2xy + y² when x = 7 and y = 3.
31. 31.If a − b = 6 and ab = 7, what is a² + b²?
32. 32.Use (a + b)(a − b) = a² − b² to find 31 × 29.
33. 33.Use (a + b)(a − b) = a² − b² to find 102 × 98.
34. 34.Use (a + b)(a − b) = a² − b² to find 72 × 68.
35. 35.Use (a + b)(a − b) = a² − b² to find 32 × 28.
36. 36.Use (a − b)² = a² − 2ab + b² to find 98².
37. 37.If a + b = 21 and ab = 108, what is a² + b²?
38. 38.Use (a − b)² = a² − 2ab + b² to find 72².
39. 39.Use (a + b)² = a² + 2ab + b² to find 101².
40. 40.Use (a − b)² = a² − 2ab + b² to find 13².

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