Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 293 · 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 = 3 and y = 2.
2. 2.Find the value of x² − y² when x = 5 and y = 2.
3. 3.Find the value of x² + 2xy + y² when x = 7 and y = 1.
4. 4.Use a² − b² = (a + b)(a − b) to find 22² − 4².
5. 5.Use (a + b)(a − b) = a² − b² to find 27 × 13.
6. 6.Use (a + b)² = a² + 2ab + b² to find 109².
7. 7.Use (a − b)² = a² − 2ab + b² to find 32².
8. 8.Find the value of x² − y² when x = 3 and y = 1.
9. 9.If a + b = 8 and ab = 15, what is a² + b²?
10. 10.Use (a − b)² = a² − 2ab + b² to find 27².
11. 11.Use a² − b² = (a + b)(a − b) to find 83² − 69².
12. 12.Use (a − b)² = a² − 2ab + b² to find 55².
13. 13.Use (a + b)² = a² + 2ab + b² to find 94².
14. 14.Use (a + b)² = a² + 2ab + b² to find 16².
15. 15.Use (a + b)(a − b) = a² − b² to find 62 × 58.
16. 16.Use (a + b)² = a² + 2ab + b² to find 52².
17. 17.Use a² − b² = (a + b)(a − b) to find 84² − 64².
18. 18.Use (a + b)(a − b) = a² − b² to find 43 × 37.
19. 19.Use a² − b² = (a + b)(a − b) to find 35² − 18².
20. 20.Use (a + b)² = a² + 2ab + b² to find 53².
21. 21.If a + b = 7 and ab = 10, what is a² + b²?
22. 22.Use (a + b)² = a² + 2ab + b² to find 72².
23. 23.Use (a + b)(a − b) = a² − b² to find 68 × 52.
24. 24.If a + b = 9 and ab = 20, what is a² + b²?
25. 25.If a + b = 3 and ab = 2, what is a² + b²?
26. 26.Find the value of x² − y² when x = 10 and y = 2.
27. 27.Use (a + b)² = a² + 2ab + b² to find 103².
28. 28.If a + b = 6 and ab = 8, what is a² + b²?
29. 29.Use (a − b)² = a² − 2ab + b² to find 15².
30. 30.Use (a − b)² = a² − 2ab + b² to find 31².
31. 31.If a + b = 12 and ab = 35, what is a² + b²?
32. 32.Use (a − b)² = a² − 2ab + b² to find 89².
33. 33.Use a² − b² = (a + b)(a − b) to find 78² − 37².
34. 34.Use (a + b)(a − b) = a² − b² to find 96 × 84.
35. 35.Use a² − b² = (a + b)(a − b) to find 74² − 46².
36. 36.If a − b = 9 and ab = 10, what is a² + b²?
37. 37.Use (a − b)² = a² − 2ab + b² to find 17².
38. 38.Use (a + b)(a − b) = a² − b² to find 66 × 54.
39. 39.Find the value of x² + 2xy + y² when x = 13 and y = 10.
40. 40.If a + b = 15 and ab = 54, what is a² + b²?

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