Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 600 · 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.Use (a − b)² = a² − 2ab + b² to find 75².
3. 3.Use (a + b)(a − b) = a² − b² to find 66 × 54.
4. 4.Use (a + b)(a − b) = a² − b² to find 107 × 93.
5. 5.Use (a − b)² = a² − 2ab + b² to find 49².
6. 6.If a − b = 5 and ab = 24, what is a² + b²?
7. 7.Use (a + b)(a − b) = a² − b² to find 57 × 43.
8. 8.If a − b = 2 and ab = 3, what is a² + b²?
9. 9.Use (a + b)² = a² + 2ab + b² to find 95².
10. 10.If a − b = 1 and ab = 2, what is a² + b²?
11. 11.If a − b = 5 and ab = 14, what is a² + b²?
12. 12.Use (a − b)² = a² − 2ab + b² to find 17².
13. 13.Find the value of x² + 2xy + y² when x = 6 and y = 4.
14. 14.Use (a + b)(a − b) = a² − b² to find 28 × 12.
15. 15.If a − b = 3 and ab = 54, what is a² + b²?
16. 16.Use (a + b)(a − b) = a² − b² to find 55 × 45.
17. 17.Use (a + b)² = a² + 2ab + b² to find 89².
18. 18.Use (a + b)² = a² + 2ab + b² to find 34².
19. 19.Use a² − b² = (a + b)(a − b) to find 78² − 1².
20. 20.Use (a + b)² = a² + 2ab + b² to find 57².
21. 21.If a − b = 3 and ab = 18, what is a² + b²?
22. 22.If a − b = 10 and ab = 24, what is a² + b²?
23. 23.Find the value of x² + 2xy + y² when x = 15 and y = 11.
24. 24.Find the value of x² − 2xy + y² when x = 5 and y = 2.
25. 25.Use (a + b)² = a² + 2ab + b² to find 32².
26. 26.Find the value of x² + 2xy + y² when x = 12 and y = 4.
27. 27.If a − b = 2 and ab = 8, what is a² + b²?
28. 28.Use (a − b)² = a² − 2ab + b² to find 39².
29. 29.Use a² − b² = (a + b)(a − b) to find 27² − 11².
30. 30.Use a² − b² = (a + b)(a − b) to find 27² − 5².
31. 31.Use (a + b)(a − b) = a² − b² to find 71 × 69.
32. 32.Use (a + b)² = a² + 2ab + b² to find 49².
33. 33.Use (a − b)² = a² − 2ab + b² to find 54².
34. 34.Find the value of x² − 2xy + y² when x = 14 and y = 12.
35. 35.Use (a + b)² = a² + 2ab + b² to find 101².
36. 36.Use a² − b² = (a + b)(a − b) to find 91² − 8².
37. 37.Find the value of x² − 2xy + y² when x = 3 and y = 2.
38. 38.Find the value of x² + 2xy + y² when x = 3 and y = 1.
39. 39.Use (a + b)² = a² + 2ab + b² to find 55².
40. 40.Use a² − b² = (a + b)(a − b) to find 59² − 18².

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