Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 128 · 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 = 3 and y = 1.
2. 2.Use (a + b)(a − b) = a² − b² to find 27 × 13.
3. 3.Use (a − b)² = a² − 2ab + b² to find 57².
4. 4.Use (a − b)² = a² − 2ab + b² to find 92².
5. 5.Use (a + b)(a − b) = a² − b² to find 78 × 62.
6. 6.Use (a + b)(a − b) = a² − b² to find 74 × 66.
7. 7.Find the value of x² − 2xy + y² when x = 7 and y = 5.
8. 8.Find the value of x² + 2xy + y² when x = 3 and y = 2.
9. 9.Use (a − b)² = a² − 2ab + b² to find 16².
10. 10.Use (a − b)² = a² − 2ab + b² to find 51².
11. 11.Find the value of x² + 2xy + y² when x = 5 and y = 1.
12. 12.If a − b = 7 and ab = 30, what is a² + b²?
13. 13.Use (a − b)² = a² − 2ab + b² to find 26².
14. 14.Use a² − b² = (a + b)(a − b) to find 83² − 31².
15. 15.Find the value of x² − 2xy + y² when x = 9 and y = 2.
16. 16.If a − b = 3 and ab = 88, what is a² + b²?
17. 17.If a + b = 17 and ab = 70, what is a² + b²?
18. 18.Use (a + b)(a − b) = a² − b² to find 46 × 34.
19. 19.Use (a + b)(a − b) = a² − b² to find 72 × 68.
20. 20.Use (a − b)² = a² − 2ab + b² to find 13².
21. 21.Use (a + b)² = a² + 2ab + b² to find 72².
22. 22.Use (a + b)² = a² + 2ab + b² to find 44².
23. 23.Use (a + b)(a − b) = a² − b² to find 73 × 67.
24. 24.Use a² − b² = (a + b)(a − b) to find 58² − 5².
25. 25.Find the value of x² + 2xy + y² when x = 7 and y = 4.
26. 26.Use a² − b² = (a + b)(a − b) to find 89² − 34².
27. 27.Use (a − b)² = a² − 2ab + b² to find 55².
28. 28.If a + b = 13 and ab = 30, what is a² + b²?
29. 29.Use (a + b)(a − b) = a² − b² to find 21 × 19.
30. 30.If a + b = 10 and ab = 21, what is a² + b²?
31. 31.Use (a + b)(a − b) = a² − b² to find 45 × 35.
32. 32.Find the value of x² − 2xy + y² when x = 9 and y = 1.
33. 33.Use a² − b² = (a + b)(a − b) to find 73² − 48².
34. 34.If a + b = 4 and ab = 3, what is a² + b²?
35. 35.Use (a − b)² = a² − 2ab + b² to find 18².
36. 36.If a + b = 12 and ab = 35, what is a² + b²?
37. 37.Use (a + b)² = a² + 2ab + b² to find 105².
38. 38.Use (a − b)² = a² − 2ab + b² to find 49².
39. 39.Use (a + b)(a − b) = a² − b² to find 22 × 18.
40. 40.Use (a + b)² = a² + 2ab + b² to find 107².

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