Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 109 · 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 23².
2. 2.Use (a + b)² = a² + 2ab + b² to find 31².
3. 3.Use (a − b)² = a² − 2ab + b² to find 81².
4. 4.Use a² − b² = (a + b)(a − b) to find 56² − 46².
5. 5.Use a² − b² = (a + b)(a − b) to find 37² − 3².
6. 6.Use (a + b)² = a² + 2ab + b² to find 19².
7. 7.Use (a − b)² = a² − 2ab + b² to find 12².
8. 8.Use (a + b)(a − b) = a² − b² to find 64 × 56.
9. 9.Use a² − b² = (a + b)(a − b) to find 50² − 39².
10. 10.Find the value of x² + 2xy + y² when x = 13 and y = 11.
11. 11.If a + b = 17 and ab = 66, what is a² + b²?
12. 12.Use (a − b)² = a² − 2ab + b² to find 95².
13. 13.Use (a + b)(a − b) = a² − b² to find 58 × 42.
14. 14.Use a² − b² = (a + b)(a − b) to find 31² − 30².
15. 15.Use (a − b)² = a² − 2ab + b² to find 44².
16. 16.Use (a + b)² = a² + 2ab + b² to find 73².
17. 17.Use (a + b)² = a² + 2ab + b² to find 49².
18. 18.Find the value of x² − y² when x = 9 and y = 3.
19. 19.Use (a + b)² = a² + 2ab + b² to find 14².
20. 20.Use (a + b)(a − b) = a² − b² to find 88 × 72.
21. 21.Use (a + b)² = a² + 2ab + b² to find 13².
22. 22.Use (a + b)² = a² + 2ab + b² to find 84².
23. 23.Use a² − b² = (a + b)(a − b) to find 72² − 1².
24. 24.Find the value of x² − 2xy + y² when x = 13 and y = 1.
25. 25.Use a² − b² = (a + b)(a − b) to find 35² − 21².
26. 26.If a + b = 13 and ab = 40, what is a² + b²?
27. 27.If a − b = 2 and ab = 8, what is a² + b²?
28. 28.Use a² − b² = (a + b)(a − b) to find 58² − 2².
29. 29.Find the value of x² − 2xy + y² when x = 4 and y = 2.
30. 30.Use a² − b² = (a + b)(a − b) to find 96² − 88².
31. 31.Use a² − b² = (a + b)(a − b) to find 21² − 4².
32. 32.Use (a + b)(a − b) = a² − b² to find 45 × 35.
33. 33.Use (a + b)² = a² + 2ab + b² to find 78².
34. 34.Find the value of x² + 2xy + y² when x = 7 and y = 6.
35. 35.Use (a − b)² = a² − 2ab + b² to find 34².
36. 36.Use (a + b)(a − b) = a² − b² to find 29 × 11.
37. 37.Use (a − b)² = a² − 2ab + b² to find 77².
38. 38.Use (a + b)² = a² + 2ab + b² to find 36².
39. 39.Use (a + b)² = a² + 2ab + b² to find 108².
40. 40.Find the value of x² − 2xy + y² when x = 6 and y = 2.

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