Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 874 · 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)² = a² − 2ab + b² to find 47².
2. 2.If a − b = 1 and ab = 90, what is a² + b²?
3. 3.Use (a − b)² = a² − 2ab + b² to find 21².
4. 4.Find the value of x² + 2xy + y² when x = 15 and y = 7.
5. 5.Use (a + b)² = a² + 2ab + b² to find 38².
6. 6.Use (a + b)² = a² + 2ab + b² to find 32².
7. 7.Use (a − b)² = a² − 2ab + b² to find 46².
8. 8.If a − b = 1 and ab = 72, what is a² + b²?
9. 9.Use (a + b)² = a² + 2ab + b² to find 102².
10. 10.If a + b = 16 and ab = 63, what is a² + b²?
11. 11.Use a² − b² = (a + b)(a − b) to find 33² − 1².
12. 12.Use (a − b)² = a² − 2ab + b² to find 45².
13. 13.Use (a + b)(a − b) = a² − b² to find 63 × 57.
14. 14.Use (a + b)² = a² + 2ab + b² to find 91².
15. 15.Use (a + b)² = a² + 2ab + b² to find 11².
16. 16.Find the value of x² − y² when x = 3 and y = 1.
17. 17.Use (a − b)² = a² − 2ab + b² to find 77².
18. 18.Find the value of x² − y² when x = 12 and y = 10.
19. 19.Use (a − b)² = a² − 2ab + b² to find 17².
20. 20.Find the value of x² + 2xy + y² when x = 14 and y = 8.
21. 21.If a + b = 10 and ab = 24, what is a² + b²?
22. 22.Use a² − b² = (a + b)(a − b) to find 78² − 21².
23. 23.Use a² − b² = (a + b)(a − b) to find 27² − 15².
24. 24.If a + b = 10 and ab = 16, what is a² + b²?
25. 25.Use a² − b² = (a + b)(a − b) to find 65² − 29².
26. 26.Use (a + b)² = a² + 2ab + b² to find 29².
27. 27.Find the value of x² − 2xy + y² when x = 9 and y = 6.
28. 28.Use (a + b)² = a² + 2ab + b² to find 49².
29. 29.If a + b = 6 and ab = 5, what is a² + b²?
30. 30.Use (a − b)² = a² − 2ab + b² to find 86².
31. 31.Use (a + b)² = a² + 2ab + b² to find 16².
32. 32.Use (a − b)² = a² − 2ab + b² to find 31².
33. 33.Use a² − b² = (a + b)(a − b) to find 24² − 8².
34. 34.If a + b = 3 and ab = 2, what is a² + b²?
35. 35.If a − b = 5 and ab = 50, what is a² + b²?
36. 36.Use (a − b)² = a² − 2ab + b² to find 11².
37. 37.If a − b = 4 and ab = 21, what is a² + b²?
38. 38.Use (a + b)(a − b) = a² − b² to find 39 × 21.
39. 39.If a + b = 13 and ab = 42, what is a² + b²?
40. 40.Use (a − b)² = a² − 2ab + b² to find 69².

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