Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 238 · 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 82².
2. 2.Use (a + b)(a − b) = a² − b² to find 48 × 32.
3. 3.Find the value of x² − 2xy + y² when x = 10 and y = 1.
4. 4.If a − b = 8 and ab = 33, what is a² + b²?
5. 5.Use (a − b)² = a² − 2ab + b² to find 37².
6. 6.Find the value of x² − y² when x = 6 and y = 3.
7. 7.If a + b = 3 and ab = 2, what is a² + b²?
8. 8.Use (a + b)² = a² + 2ab + b² to find 41².
9. 9.Use a² − b² = (a + b)(a − b) to find 39² − 36².
10. 10.Find the value of x² − 2xy + y² when x = 5 and y = 3.
11. 11.Find the value of x² − 2xy + y² when x = 14 and y = 9.
12. 12.If a − b = 2 and ab = 3, what is a² + b²?
13. 13.Use (a + b)² = a² + 2ab + b² to find 103².
14. 14.Use (a − b)² = a² − 2ab + b² to find 69².
15. 15.Find the value of x² + 2xy + y² when x = 13 and y = 6.
16. 16.Use (a − b)² = a² − 2ab + b² to find 54².
17. 17.Use a² − b² = (a + b)(a − b) to find 87² − 86².
18. 18.Use (a + b)(a − b) = a² − b² to find 107 × 93.
19. 19.Find the value of x² − y² when x = 6 and y = 4.
20. 20.Find the value of x² − 2xy + y² when x = 7 and y = 4.
21. 21.Find the value of x² + 2xy + y² when x = 14 and y = 10.
22. 22.If a + b = 20 and ab = 96, what is a² + b²?
23. 23.Use (a + b)(a − b) = a² − b² to find 108 × 92.
24. 24.Use (a + b)² = a² + 2ab + b² to find 83².
25. 25.Use a² − b² = (a + b)(a − b) to find 61² − 16².
26. 26.Use (a + b)² = a² + 2ab + b² to find 67².
27. 27.If a + b = 13 and ab = 36, what is a² + b²?
28. 28.Find the value of x² − y² when x = 15 and y = 13.
29. 29.Use (a + b)² = a² + 2ab + b² to find 14².
30. 30.Use (a + b)(a − b) = a² − b² to find 41 × 39.
31. 31.Use a² − b² = (a + b)(a − b) to find 55² − 41².
32. 32.Use (a − b)² = a² − 2ab + b² to find 38².
33. 33.Use (a + b)² = a² + 2ab + b² to find 38².
34. 34.Use (a + b)² = a² + 2ab + b² to find 104².
35. 35.Use (a − b)² = a² − 2ab + b² to find 47².
36. 36.Use (a + b)(a − b) = a² − b² to find 109 × 91.
37. 37.Use (a + b)² = a² + 2ab + b² to find 45².
38. 38.Use (a − b)² = a² − 2ab + b² to find 76².
39. 39.Find the value of x² + 2xy + y² when x = 5 and y = 3.
40. 40.Use a² − b² = (a + b)(a − b) to find 62² − 25².

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