Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 788 · 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 = 23 and ab = 132, what is a² + b²?
2. 2.Find the value of x² − y² when x = 3 and y = 1.
3. 3.Use (a − b)² = a² − 2ab + b² to find 68².
4. 4.Use (a − b)² = a² − 2ab + b² to find 81².
5. 5.Use (a − b)² = a² − 2ab + b² to find 33².
6. 6.Find the value of x² − 2xy + y² when x = 14 and y = 7.
7. 7.Use (a + b)² = a² + 2ab + b² to find 82².
8. 8.If a + b = 9 and ab = 14, what is a² + b²?
9. 9.Find the value of x² − y² when x = 12 and y = 5.
10. 10.Find the value of x² − y² when x = 4 and y = 2.
11. 11.Use (a − b)² = a² − 2ab + b² to find 31².
12. 12.If a − b = 3 and ab = 10, what is a² + b²?
13. 13.If a + b = 5 and ab = 4, what is a² + b²?
14. 14.If a − b = 2 and ab = 99, what is a² + b²?
15. 15.Use a² − b² = (a + b)(a − b) to find 77² − 45².
16. 16.Use a² − b² = (a + b)(a − b) to find 90² − 31².
17. 17.Use (a + b)(a − b) = a² − b² to find 106 × 94.
18. 18.Use a² − b² = (a + b)(a − b) to find 91² − 43².
19. 19.Use (a − b)² = a² − 2ab + b² to find 91².
20. 20.Use (a + b)² = a² + 2ab + b² to find 34².
21. 21.Use a² − b² = (a + b)(a − b) to find 21² − 8².
22. 22.Use a² − b² = (a + b)(a − b) to find 64² − 36².
23. 23.Use (a + b)(a − b) = a² − b² to find 89 × 71.
24. 24.Find the value of x² + 2xy + y² when x = 10 and y = 1.
25. 25.Find the value of x² − 2xy + y² when x = 3 and y = 2.
26. 26.Find the value of x² + 2xy + y² when x = 5 and y = 3.
27. 27.Find the value of x² − y² when x = 14 and y = 8.
28. 28.Use (a − b)² = a² − 2ab + b² to find 51².
29. 29.Use a² − b² = (a + b)(a − b) to find 29² − 23².
30. 30.Use a² − b² = (a + b)(a − b) to find 86² − 36².
31. 31.Use a² − b² = (a + b)(a − b) to find 60² − 9².
32. 32.Use (a − b)² = a² − 2ab + b² to find 78².
33. 33.Use (a − b)² = a² − 2ab + b² to find 94².
34. 34.Use a² − b² = (a + b)(a − b) to find 49² − 23².
35. 35.Use (a − b)² = a² − 2ab + b² to find 37².
36. 36.Use (a − b)² = a² − 2ab + b² to find 64².
37. 37.If a − b = 1 and ab = 12, what is a² + b²?
38. 38.If a + b = 12 and ab = 20, what is a² + b²?
39. 39.Use (a − b)² = a² − 2ab + b² to find 85².
40. 40.Find the value of x² + 2xy + y² when x = 10 and y = 8.

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