Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 199 · 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.If a − b = 2 and ab = 3, what is a² + b²?
2. 2.If a − b = 2 and ab = 63, what is a² + b²?
3. 3.Use a² − b² = (a + b)(a − b) to find 84² − 24².
4. 4.Use (a − b)² = a² − 2ab + b² to find 46².
5. 5.Find the value of x² − 2xy + y² when x = 14 and y = 8.
6. 6.Use (a − b)² = a² − 2ab + b² to find 38².
7. 7.Use (a + b)(a − b) = a² − b² to find 95 × 85.
8. 8.Use (a − b)² = a² − 2ab + b² to find 79².
9. 9.Use (a + b)² = a² + 2ab + b² to find 26².
10. 10.Use a² − b² = (a + b)(a − b) to find 28² − 14².
11. 11.Use a² − b² = (a + b)(a − b) to find 85² − 47².
12. 12.Find the value of x² − 2xy + y² when x = 5 and y = 3.
13. 13.Use (a − b)² = a² − 2ab + b² to find 83².
14. 14.Use a² − b² = (a + b)(a − b) to find 56² − 6².
15. 15.Use (a + b)² = a² + 2ab + b² to find 45².
16. 16.Use (a + b)² = a² + 2ab + b² to find 73².
17. 17.If a + b = 11 and ab = 24, what is a² + b²?
18. 18.Use (a + b)² = a² + 2ab + b² to find 92².
19. 19.Use (a + b)(a − b) = a² − b² to find 41 × 39.
20. 20.Use (a − b)² = a² − 2ab + b² to find 41².
21. 21.Use (a − b)² = a² − 2ab + b² to find 76².
22. 22.Find the value of x² + 2xy + y² when x = 13 and y = 5.
23. 23.Use (a + b)² = a² + 2ab + b² to find 54².
24. 24.Use (a + b)(a − b) = a² − b² to find 62 × 58.
25. 25.Use (a − b)² = a² − 2ab + b² to find 65².
26. 26.Use (a − b)² = a² − 2ab + b² to find 89².
27. 27.If a + b = 3 and ab = 2, what is a² + b²?
28. 28.Use (a + b)(a − b) = a² − b² to find 37 × 23.
29. 29.If a − b = 7 and ab = 30, what is a² + b²?
30. 30.Use (a + b)² = a² + 2ab + b² to find 62².
31. 31.Use a² − b² = (a + b)(a − b) to find 84² − 20².
32. 32.If a + b = 9 and ab = 8, what is a² + b²?
33. 33.If a − b = 3 and ab = 28, what is a² + b²?
34. 34.If a − b = 2 and ab = 8, what is a² + b²?
35. 35.Use a² − b² = (a + b)(a − b) to find 76² − 73².
36. 36.Use (a + b)² = a² + 2ab + b² to find 43².
37. 37.Use (a − b)² = a² − 2ab + b² to find 99².
38. 38.Use (a + b)(a − b) = a² − b² to find 88 × 72.
39. 39.Use (a + b)² = a² + 2ab + b² to find 85².
40. 40.Find the value of x² − y² when x = 10 and y = 1.

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