Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 166 · 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 = 4 and y = 2.
2. 2.Use (a − b)² = a² − 2ab + b² to find 11².
3. 3.Find the value of x² + 2xy + y² when x = 3 and y = 2.
4. 4.Use a² − b² = (a + b)(a − b) to find 76² − 19².
5. 5.Use (a − b)² = a² − 2ab + b² to find 57².
6. 6.Find the value of x² + 2xy + y² when x = 6 and y = 5.
7. 7.Use (a + b)(a − b) = a² − b² to find 24 × 16.
8. 8.Find the value of x² − y² when x = 4 and y = 3.
9. 9.Find the value of x² − y² when x = 10 and y = 7.
10. 10.Use a² − b² = (a + b)(a − b) to find 75² − 54².
11. 11.Use (a + b)² = a² + 2ab + b² to find 52².
12. 12.Use (a + b)² = a² + 2ab + b² to find 48².
13. 13.Use (a + b)² = a² + 2ab + b² to find 36².
14. 14.Find the value of x² + 2xy + y² when x = 13 and y = 3.
15. 15.Use (a + b)² = a² + 2ab + b² to find 41².
16. 16.Use (a + b)² = a² + 2ab + b² to find 31².
17. 17.Use (a − b)² = a² − 2ab + b² to find 68².
18. 18.Use (a − b)² = a² − 2ab + b² to find 18².
19. 19.Use (a + b)(a − b) = a² − b² to find 23 × 17.
20. 20.Use (a + b)² = a² + 2ab + b² to find 13².
21. 21.Use (a + b)(a − b) = a² − b² to find 93 × 87.
22. 22.Use (a + b)(a − b) = a² − b² to find 53 × 47.
23. 23.Use (a − b)² = a² − 2ab + b² to find 13².
24. 24.If a − b = 2 and ab = 3, what is a² + b²?
25. 25.Use (a − b)² = a² − 2ab + b² to find 88².
26. 26.Use (a − b)² = a² − 2ab + b² to find 39².
27. 27.Use (a + b)² = a² + 2ab + b² to find 78².
28. 28.If a − b = 8 and ab = 48, what is a² + b²?
29. 29.Use (a + b)(a − b) = a² − b² to find 97 × 83.
30. 30.If a + b = 11 and ab = 10, what is a² + b²?
31. 31.Use a² − b² = (a + b)(a − b) to find 54² − 1².
32. 32.Use (a − b)² = a² − 2ab + b² to find 77².
33. 33.Use a² − b² = (a + b)(a − b) to find 83² − 29².
34. 34.If a + b = 8 and ab = 7, what is a² + b²?
35. 35.Use (a + b)(a − b) = a² − b² to find 108 × 92.
36. 36.Use (a + b)(a − b) = a² − b² to find 91 × 89.
37. 37.If a − b = 2 and ab = 8, what is a² + b²?
38. 38.Use (a + b)(a − b) = a² − b² to find 62 × 58.
39. 39.Use (a − b)² = a² − 2ab + b² to find 66².
40. 40.Use (a + b)² = a² + 2ab + b² to find 96².

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