Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 857 · 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 95².
2. 2.Use (a + b)² = a² + 2ab + b² to find 94².
3. 3.Use a² − b² = (a + b)(a − b) to find 64² − 21².
4. 4.If a − b = 2 and ab = 8, what is a² + b²?
5. 5.Use (a + b)² = a² + 2ab + b² to find 61².
6. 6.Use (a − b)² = a² − 2ab + b² to find 14².
7. 7.Use (a − b)² = a² − 2ab + b² to find 19².
8. 8.Use (a − b)² = a² − 2ab + b² to find 45².
9. 9.Use a² − b² = (a + b)(a − b) to find 34² − 9².
10. 10.Find the value of x² − 2xy + y² when x = 7 and y = 3.
11. 11.Use (a − b)² = a² − 2ab + b² to find 66².
12. 12.Use a² − b² = (a + b)(a − b) to find 53² − 7².
13. 13.Find the value of x² − 2xy + y² when x = 9 and y = 6.
14. 14.Use (a − b)² = a² − 2ab + b² to find 33².
15. 15.If a − b = 8 and ab = 9, what is a² + b²?
16. 16.Find the value of x² − 2xy + y² when x = 9 and y = 1.
17. 17.Find the value of x² − y² when x = 4 and y = 2.
18. 18.Use (a − b)² = a² − 2ab + b² to find 76².
19. 19.Use a² − b² = (a + b)(a − b) to find 91² − 37².
20. 20.Use (a + b)(a − b) = a² − b² to find 23 × 17.
21. 21.If a − b = 3 and ab = 4, what is a² + b²?
22. 22.Use (a + b)² = a² + 2ab + b² to find 76².
23. 23.Use (a − b)² = a² − 2ab + b² to find 72².
24. 24.Use a² − b² = (a + b)(a − b) to find 54² − 31².
25. 25.Use (a − b)² = a² − 2ab + b² to find 54².
26. 26.Use (a + b)² = a² + 2ab + b² to find 44².
27. 27.Use (a + b)(a − b) = a² − b² to find 29 × 11.
28. 28.Use (a − b)² = a² − 2ab + b² to find 24².
29. 29.Find the value of x² + 2xy + y² when x = 7 and y = 4.
30. 30.If a − b = 8 and ab = 48, what is a² + b²?
31. 31.Use (a + b)² = a² + 2ab + b² to find 82².
32. 32.Use (a + b)(a − b) = a² − b² to find 27 × 13.
33. 33.Use (a + b)(a − b) = a² − b² to find 84 × 76.
34. 34.Find the value of x² + 2xy + y² when x = 6 and y = 4.
35. 35.Find the value of x² + 2xy + y² when x = 14 and y = 11.
36. 36.Use (a + b)² = a² + 2ab + b² to find 68².
37. 37.Find the value of x² + 2xy + y² when x = 13 and y = 7.
38. 38.If a + b = 3 and ab = 2, what is a² + b²?
39. 39.Use (a − b)² = a² − 2ab + b² to find 75².
40. 40.Find the value of x² + 2xy + y² when x = 11 and y = 8.

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