Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 13 · 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 = 7 and ab = 60, what is a² + b²?
2. 2.Use (a + b)² = a² + 2ab + b² to find 104².
3. 3.Use (a − b)² = a² − 2ab + b² to find 51².
4. 4.Use a² − b² = (a + b)(a − b) to find 36² − 18².
5. 5.Use (a + b)² = a² + 2ab + b² to find 29².
6. 6.Use (a + b)(a − b) = a² − b² to find 47 × 33.
7. 7.If a + b = 8 and ab = 15, what is a² + b²?
8. 8.If a + b = 3 and ab = 2, what is a² + b²?
9. 9.If a + b = 4 and ab = 3, what is a² + b²?
10. 10.Use (a + b)(a − b) = a² − b² to find 66 × 54.
11. 11.Find the value of x² + 2xy + y² when x = 15 and y = 4.
12. 12.Use (a − b)² = a² − 2ab + b² to find 79².
13. 13.Find the value of x² − y² when x = 14 and y = 13.
14. 14.Use (a − b)² = a² − 2ab + b² to find 86².
15. 15.Use (a − b)² = a² − 2ab + b² to find 19².
16. 16.Use a² − b² = (a + b)(a − b) to find 39² − 1².
17. 17.Use (a + b)² = a² + 2ab + b² to find 102².
18. 18.Find the value of x² + 2xy + y² when x = 7 and y = 1.
19. 19.Find the value of x² − y² when x = 3 and y = 2.
20. 20.If a + b = 8 and ab = 12, what is a² + b²?
21. 21.Use (a + b)(a − b) = a² − b² to find 73 × 67.
22. 22.Use (a + b)² = a² + 2ab + b² to find 61².
23. 23.If a − b = 2 and ab = 3, what is a² + b²?
24. 24.Use (a + b)² = a² + 2ab + b² to find 95².
25. 25.If a − b = 6 and ab = 16, what is a² + b²?
26. 26.Find the value of x² − y² when x = 8 and y = 7.
27. 27.Use (a − b)² = a² − 2ab + b² to find 52².
28. 28.Use (a + b)(a − b) = a² − b² to find 57 × 43.
29. 29.Use (a − b)² = a² − 2ab + b² to find 64².
30. 30.Use (a − b)² = a² − 2ab + b² to find 14².
31. 31.If a + b = 22 and ab = 120, what is a² + b²?
32. 32.Find the value of x² + 2xy + y² when x = 6 and y = 5.
33. 33.Use (a + b)(a − b) = a² − b² to find 68 × 52.
34. 34.Use (a − b)² = a² − 2ab + b² to find 32².
35. 35.Find the value of x² + 2xy + y² when x = 3 and y = 2.
36. 36.Use (a + b)² = a² + 2ab + b² to find 31².
37. 37.Use (a + b)(a − b) = a² − b² to find 95 × 85.
38. 38.Use (a − b)² = a² − 2ab + b² to find 31².
39. 39.Use a² − b² = (a + b)(a − b) to find 66² − 6².
40. 40.Find the value of x² − 2xy + y² when x = 12 and y = 4.

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