Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 766 · 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 = 13 and ab = 36, what is a² + b²?
2. 2.If a − b = 1 and ab = 72, what is a² + b²?
3. 3.Use (a + b)² = a² + 2ab + b² to find 72².
4. 4.Use (a − b)² = a² − 2ab + b² to find 23².
5. 5.Use (a − b)² = a² − 2ab + b² to find 78².
6. 6.Use a² − b² = (a + b)(a − b) to find 27² − 7².
7. 7.Use (a − b)² = a² − 2ab + b² to find 99².
8. 8.Find the value of x² − 2xy + y² when x = 11 and y = 3.
9. 9.Use (a + b)(a − b) = a² − b² to find 31 × 29.
10. 10.Use a² − b² = (a + b)(a − b) to find 24² − 1².
11. 11.Use (a − b)² = a² − 2ab + b² to find 51².
12. 12.Find the value of x² + 2xy + y² when x = 5 and y = 1.
13. 13.Use (a + b)² = a² + 2ab + b² to find 18².
14. 14.Use (a + b)² = a² + 2ab + b² to find 84².
15. 15.Find the value of x² − y² when x = 13 and y = 4.
16. 16.Use (a − b)² = a² − 2ab + b² to find 76².
17. 17.Use (a + b)² = a² + 2ab + b² to find 28².
18. 18.Use a² − b² = (a + b)(a − b) to find 50² − 12².
19. 19.Use a² − b² = (a + b)(a − b) to find 83² − 75².
20. 20.Find the value of x² − y² when x = 8 and y = 1.
21. 21.Use (a + b)(a − b) = a² − b² to find 92 × 88.
22. 22.Use (a + b)² = a² + 2ab + b² to find 97².
23. 23.Use (a − b)² = a² − 2ab + b² to find 64².
24. 24.Use (a + b)(a − b) = a² − b² to find 41 × 39.
25. 25.If a − b = 1 and ab = 42, what is a² + b²?
26. 26.Use (a + b)(a − b) = a² − b² to find 66 × 54.
27. 27.Use (a − b)² = a² − 2ab + b² to find 43².
28. 28.Use (a − b)² = a² − 2ab + b² to find 16².
29. 29.Find the value of x² + 2xy + y² when x = 13 and y = 7.
30. 30.Use (a − b)² = a² − 2ab + b² to find 54².
31. 31.Use (a + b)(a − b) = a² − b² to find 75 × 65.
32. 32.If a − b = 7 and ab = 60, what is a² + b²?
33. 33.Find the value of x² − 2xy + y² when x = 15 and y = 3.
34. 34.Find the value of x² + 2xy + y² when x = 10 and y = 3.
35. 35.Use (a + b)(a − b) = a² − b² to find 103 × 97.
36. 36.Find the value of x² − y² when x = 8 and y = 5.
37. 37.Use (a − b)² = a² − 2ab + b² to find 31².
38. 38.Find the value of x² − y² when x = 9 and y = 6.
39. 39.Use (a + b)(a − b) = a² − b² to find 34 × 26.
40. 40.If a − b = 1 and ab = 2, what is a² + b²?

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