Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 871 · 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 a² − b² = (a + b)(a − b) to find 31² − 4².
2. 2.Find the value of x² − y² when x = 15 and y = 5.
3. 3.Use (a − b)² = a² − 2ab + b² to find 69².
4. 4.If a − b = 3 and ab = 18, what is a² + b²?
5. 5.Use (a − b)² = a² − 2ab + b² to find 76².
6. 6.Use (a + b)(a − b) = a² − b² to find 48 × 32.
7. 7.Use (a + b)(a − b) = a² − b² to find 104 × 96.
8. 8.Use (a + b)(a − b) = a² − b² to find 81 × 79.
9. 9.Use (a + b)² = a² + 2ab + b² to find 44².
10. 10.Use (a + b)² = a² + 2ab + b² to find 87².
11. 11.Use (a + b)² = a² + 2ab + b² to find 61².
12. 12.Use (a + b)² = a² + 2ab + b² to find 14².
13. 13.Use a² − b² = (a + b)(a − b) to find 75² − 7².
14. 14.Use (a + b)² = a² + 2ab + b² to find 31².
15. 15.Use (a + b)(a − b) = a² − b² to find 54 × 46.
16. 16.Use (a + b)(a − b) = a² − b² to find 68 × 52.
17. 17.Use a² − b² = (a + b)(a − b) to find 51² − 17².
18. 18.Use (a − b)² = a² − 2ab + b² to find 44².
19. 19.Use (a + b)(a − b) = a² − b² to find 76 × 64.
20. 20.Use (a + b)² = a² + 2ab + b² to find 12².
21. 21.Use (a − b)² = a² − 2ab + b² to find 71².
22. 22.Find the value of x² − y² when x = 10 and y = 2.
23. 23.Find the value of x² − y² when x = 5 and y = 1.
24. 24.Use (a + b)(a − b) = a² − b² to find 44 × 36.
25. 25.Use (a + b)² = a² + 2ab + b² to find 65².
26. 26.Use (a − b)² = a² − 2ab + b² to find 67².
27. 27.Use (a + b)² = a² + 2ab + b² to find 37².
28. 28.Use (a − b)² = a² − 2ab + b² to find 31².
29. 29.Find the value of x² − 2xy + y² when x = 15 and y = 9.
30. 30.If a − b = 5 and ab = 66, what is a² + b²?
31. 31.Find the value of x² + 2xy + y² when x = 5 and y = 4.
32. 32.Use a² − b² = (a + b)(a − b) to find 28² − 1².
33. 33.If a + b = 20 and ab = 96, what is a² + b²?
34. 34.If a + b = 5 and ab = 6, what is a² + b²?
35. 35.Use a² − b² = (a + b)(a − b) to find 52² − 49².
36. 36.Use a² − b² = (a + b)(a − b) to find 73² − 62².
37. 37.Find the value of x² − y² when x = 6 and y = 4.
38. 38.Use (a − b)² = a² − 2ab + b² to find 25².
39. 39.Use (a + b)² = a² + 2ab + b² to find 17².
40. 40.If a + b = 10 and ab = 16, what is a² + b²?

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