Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 278 · 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 a² − b² = (a + b)(a − b) to find 22² − 19².
2. 2.Use (a + b)² = a² + 2ab + b² to find 39².
3. 3.Use a² − b² = (a + b)(a − b) to find 70² − 18².
4. 4.Use (a + b)(a − b) = a² − b² to find 26 × 14.
5. 5.Use a² − b² = (a + b)(a − b) to find 86² − 24².
6. 6.If a + b = 11 and ab = 10, what is a² + b²?
7. 7.Use (a − b)² = a² − 2ab + b² to find 42².
8. 8.If a + b = 12 and ab = 11, what is a² + b²?
9. 9.If a + b = 17 and ab = 72, what is a² + b²?
10. 10.Use (a + b)(a − b) = a² − b² to find 74 × 66.
11. 11.Use a² − b² = (a + b)(a − b) to find 69² − 35².
12. 12.Find the value of x² − y² when x = 10 and y = 1.
13. 13.Use (a − b)² = a² − 2ab + b² to find 56².
14. 14.Find the value of x² − 2xy + y² when x = 3 and y = 1.
15. 15.Use (a + b)² = a² + 2ab + b² to find 38².
16. 16.If a − b = 8 and ab = 9, what is a² + b²?
17. 17.Use (a − b)² = a² − 2ab + b² to find 89².
18. 18.If a − b = 2 and ab = 8, what is a² + b²?
19. 19.If a − b = 2 and ab = 15, what is a² + b²?
20. 20.Use (a + b)² = a² + 2ab + b² to find 32².
21. 21.Use (a − b)² = a² − 2ab + b² to find 95².
22. 22.Use a² − b² = (a + b)(a − b) to find 36² − 6².
23. 23.If a − b = 3 and ab = 4, what is a² + b²?
24. 24.Use (a − b)² = a² − 2ab + b² to find 28².
25. 25.Use (a − b)² = a² − 2ab + b² to find 49².
26. 26.Use (a − b)² = a² − 2ab + b² to find 51².
27. 27.Use (a + b)² = a² + 2ab + b² to find 27².
28. 28.Use (a + b)² = a² + 2ab + b² to find 16².
29. 29.If a + b = 3 and ab = 2, what is a² + b²?
30. 30.Find the value of x² − 2xy + y² when x = 9 and y = 1.
31. 31.Use (a + b)(a − b) = a² − b² to find 54 × 46.
32. 32.Use (a + b)² = a² + 2ab + b² to find 85².
33. 33.Use (a − b)² = a² − 2ab + b² to find 29².
34. 34.Use (a + b)(a − b) = a² − b² to find 85 × 75.
35. 35.Use (a − b)² = a² − 2ab + b² to find 85².
36. 36.Find the value of x² − 2xy + y² when x = 10 and y = 1.
37. 37.Find the value of x² + 2xy + y² when x = 8 and y = 4.
38. 38.Use (a + b)² = a² + 2ab + b² to find 44².
39. 39.Use a² − b² = (a + b)(a − b) to find 20² − 14².
40. 40.Use (a − b)² = a² − 2ab + b² to find 47².

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