Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 952 · 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.If a − b = 7 and ab = 44, what is a² + b²?
2. 2.Use (a − b)² = a² − 2ab + b² to find 49².
3. 3.If a − b = 2 and ab = 3, what is a² + b²?
4. 4.Use (a − b)² = a² − 2ab + b² to find 46².
5. 5.Use (a − b)² = a² − 2ab + b² to find 91².
6. 6.Use (a + b)(a − b) = a² − b² to find 73 × 67.
7. 7.Use (a + b)(a − b) = a² − b² to find 26 × 14.
8. 8.Use (a + b)(a − b) = a² − b² to find 21 × 19.
9. 9.Use (a + b)² = a² + 2ab + b² to find 85².
10. 10.Use a² − b² = (a + b)(a − b) to find 56² − 37².
11. 11.If a − b = 1 and ab = 2, what is a² + b²?
12. 12.Use a² − b² = (a + b)(a − b) to find 52² − 11².
13. 13.Find the value of x² + 2xy + y² when x = 5 and y = 4.
14. 14.Find the value of x² − y² when x = 7 and y = 5.
15. 15.Use a² − b² = (a + b)(a − b) to find 23² − 17².
16. 16.Use a² − b² = (a + b)(a − b) to find 65² − 12².
17. 17.Use (a − b)² = a² − 2ab + b² to find 25².
18. 18.If a − b = 2 and ab = 8, what is a² + b²?
19. 19.Use a² − b² = (a + b)(a − b) to find 98² − 14².
20. 20.If a − b = 10 and ab = 11, what is a² + b²?
21. 21.Use (a + b)² = a² + 2ab + b² to find 37².
22. 22.Use (a + b)² = a² + 2ab + b² to find 11².
23. 23.Use a² − b² = (a + b)(a − b) to find 59² − 24².
24. 24.Find the value of x² + 2xy + y² when x = 12 and y = 8.
25. 25.If a − b = 5 and ab = 36, what is a² + b²?
26. 26.Use (a + b)(a − b) = a² − b² to find 42 × 38.
27. 27.Use (a + b)(a − b) = a² − b² to find 32 × 28.
28. 28.Use a² − b² = (a + b)(a − b) to find 36² − 10².
29. 29.Use (a − b)² = a² − 2ab + b² to find 78².
30. 30.Use (a + b)² = a² + 2ab + b² to find 97².
31. 31.Use (a + b)(a − b) = a² − b² to find 93 × 87.
32. 32.Use (a + b)(a − b) = a² − b² to find 89 × 71.
33. 33.Find the value of x² − 2xy + y² when x = 7 and y = 2.
34. 34.Use (a − b)² = a² − 2ab + b² to find 51².
35. 35.Use (a + b)² = a² + 2ab + b² to find 64².
36. 36.Use (a + b)(a − b) = a² − b² to find 49 × 31.
37. 37.Use (a + b)(a − b) = a² − b² to find 41 × 39.
38. 38.If a − b = 1 and ab = 42, what is a² + b²?
39. 39.Find the value of x² − y² when x = 4 and y = 2.
40. 40.Use (a + b)² = a² + 2ab + b² to find 73².

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