Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 896 · 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 79².
2. 2.Use a² − b² = (a + b)(a − b) to find 42² − 25².
3. 3.Find the value of x² − 2xy + y² when x = 9 and y = 2.
4. 4.Use a² − b² = (a + b)(a − b) to find 65² − 58².
5. 5.If a + b = 6 and ab = 5, what is a² + b²?
6. 6.Use a² − b² = (a + b)(a − b) to find 55² − 31².
7. 7.Use a² − b² = (a + b)(a − b) to find 81² − 15².
8. 8.Use a² − b² = (a + b)(a − b) to find 83² − 26².
9. 9.Use (a − b)² = a² − 2ab + b² to find 99².
10. 10.If a − b = 9 and ab = 22, what is a² + b²?
11. 11.Use (a − b)² = a² − 2ab + b² to find 37².
12. 12.If a + b = 11 and ab = 18, what is a² + b²?
13. 13.If a + b = 5 and ab = 6, what is a² + b²?
14. 14.If a + b = 12 and ab = 11, what is a² + b²?
15. 15.Find the value of x² + 2xy + y² when x = 5 and y = 3.
16. 16.Use a² − b² = (a + b)(a − b) to find 86² − 35².
17. 17.Use (a − b)² = a² − 2ab + b² to find 27².
18. 18.Find the value of x² + 2xy + y² when x = 10 and y = 8.
19. 19.Use (a + b)(a − b) = a² − b² to find 43 × 37.
20. 20.Use (a − b)² = a² − 2ab + b² to find 24².
21. 21.Find the value of x² − 2xy + y² when x = 4 and y = 2.
22. 22.If a + b = 13 and ab = 22, what is a² + b²?
23. 23.Use (a + b)(a − b) = a² − b² to find 87 × 73.
24. 24.Use (a + b)² = a² + 2ab + b² to find 49².
25. 25.Use (a + b)(a − b) = a² − b² to find 78 × 62.
26. 26.Use (a + b)(a − b) = a² − b² to find 91 × 89.
27. 27.Find the value of x² − 2xy + y² when x = 14 and y = 12.
28. 28.Use a² − b² = (a + b)(a − b) to find 68² − 67².
29. 29.Use (a + b)² = a² + 2ab + b² to find 86².
30. 30.Use (a − b)² = a² − 2ab + b² to find 69².
31. 31.Use (a + b)² = a² + 2ab + b² to find 28².
32. 32.Find the value of x² − 2xy + y² when x = 5 and y = 4.
33. 33.Use (a − b)² = a² − 2ab + b² to find 32².
34. 34.Find the value of x² − y² when x = 14 and y = 6.
35. 35.Find the value of x² − y² when x = 7 and y = 4.
36. 36.Use (a + b)(a − b) = a² − b² to find 94 × 86.
37. 37.Use a² − b² = (a + b)(a − b) to find 36² − 15².
38. 38.Find the value of x² + 2xy + y² when x = 4 and y = 3.
39. 39.Use (a − b)² = a² − 2ab + b² to find 15².
40. 40.If a + b = 9 and ab = 14, what is a² + b²?

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