Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 734 · 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.Find the value of x² + 2xy + y² when x = 5 and y = 1.
2. 2.Use a² − b² = (a + b)(a − b) to find 54² − 33².
3. 3.Use (a + b)(a − b) = a² − b² to find 103 × 97.
4. 4.Use (a − b)² = a² − 2ab + b² to find 88².
5. 5.Find the value of x² − y² when x = 4 and y = 3.
6. 6.Use (a − b)² = a² − 2ab + b² to find 52².
7. 7.Use (a + b)(a − b) = a² − b² to find 94 × 86.
8. 8.If a − b = 4 and ab = 5, what is a² + b²?
9. 9.Use a² − b² = (a + b)(a − b) to find 74² − 33².
10. 10.Find the value of x² + 2xy + y² when x = 10 and y = 5.
11. 11.Use (a + b)(a − b) = a² − b² to find 57 × 43.
12. 12.Use (a + b)(a − b) = a² − b² to find 65 × 55.
13. 13.Use (a + b)² = a² + 2ab + b² to find 84².
14. 14.If a − b = 5 and ab = 6, what is a² + b²?
15. 15.Use a² − b² = (a + b)(a − b) to find 56² − 16².
16. 16.Find the value of x² + 2xy + y² when x = 10 and y = 6.
17. 17.Find the value of x² + 2xy + y² when x = 8 and y = 5.
18. 18.Use (a + b)² = a² + 2ab + b² to find 79².
19. 19.Use (a − b)² = a² − 2ab + b² to find 57².
20. 20.Use (a + b)² = a² + 2ab + b² to find 109².
21. 21.Use (a + b)² = a² + 2ab + b² to find 26².
22. 22.If a + b = 6 and ab = 8, what is a² + b²?
23. 23.Use a² − b² = (a + b)(a − b) to find 93² − 18².
24. 24.Find the value of x² + 2xy + y² when x = 15 and y = 3.
25. 25.Use (a − b)² = a² − 2ab + b² to find 36².
26. 26.Use (a + b)² = a² + 2ab + b² to find 99².
27. 27.Use (a − b)² = a² − 2ab + b² to find 99².
28. 28.Use a² − b² = (a + b)(a − b) to find 67² − 46².
29. 29.Use a² − b² = (a + b)(a − b) to find 30² − 2².
30. 30.Use (a − b)² = a² − 2ab + b² to find 53².
31. 31.Use (a + b)(a − b) = a² − b² to find 69 × 51.
32. 32.Find the value of x² − 2xy + y² when x = 15 and y = 4.
33. 33.Use (a + b)(a − b) = a² − b² to find 59 × 41.
34. 34.Use (a − b)² = a² − 2ab + b² to find 45².
35. 35.Use (a + b)² = a² + 2ab + b² to find 27².
36. 36.Use (a + b)² = a² + 2ab + b² to find 24².
37. 37.Use (a + b)(a − b) = a² − b² to find 91 × 89.
38. 38.Use (a + b)² = a² + 2ab + b² to find 107².
39. 39.Find the value of x² − 2xy + y² when x = 6 and y = 1.
40. 40.If a + b = 8 and ab = 12, what is a² + b²?

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