Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 648 · 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 (a + b)(a − b) = a² − b² to find 42 × 38.
2. 2.Use (a − b)² = a² − 2ab + b² to find 16².
3. 3.Use a² − b² = (a + b)(a − b) to find 26² − 7².
4. 4.If a − b = 5 and ab = 6, what is a² + b²?
5. 5.Use (a − b)² = a² − 2ab + b² to find 89².
6. 6.If a + b = 12 and ab = 27, what is a² + b²?
7. 7.Use (a + b)² = a² + 2ab + b² to find 19².
8. 8.Use (a + b)² = a² + 2ab + b² to find 62².
9. 9.Find the value of x² − 2xy + y² when x = 4 and y = 2.
10. 10.If a − b = 3 and ab = 70, what is a² + b²?
11. 11.Use a² − b² = (a + b)(a − b) to find 91² − 13².
12. 12.If a + b = 16 and ab = 63, what is a² + b²?
13. 13.Find the value of x² − 2xy + y² when x = 3 and y = 2.
14. 14.Find the value of x² − 2xy + y² when x = 10 and y = 8.
15. 15.If a − b = 3 and ab = 28, what is a² + b²?
16. 16.Use (a + b)(a − b) = a² − b² to find 41 × 39.
17. 17.Use (a − b)² = a² − 2ab + b² to find 82².
18. 18.Use (a − b)² = a² − 2ab + b² to find 21².
19. 19.Use (a + b)² = a² + 2ab + b² to find 26².
20. 20.Use (a − b)² = a² − 2ab + b² to find 84².
21. 21.Use (a + b)(a − b) = a² − b² to find 106 × 94.
22. 22.Use a² − b² = (a + b)(a − b) to find 78² − 61².
23. 23.Use (a + b)(a − b) = a² − b² to find 38 × 22.
24. 24.Use (a + b)² = a² + 2ab + b² to find 88².
25. 25.Find the value of x² + 2xy + y² when x = 4 and y = 2.
26. 26.Find the value of x² − 2xy + y² when x = 6 and y = 1.
27. 27.Use (a + b)² = a² + 2ab + b² to find 68².
28. 28.Use (a + b)(a − b) = a² − b² to find 43 × 37.
29. 29.Use (a + b)(a − b) = a² − b² to find 33 × 27.
30. 30.Use (a + b)² = a² + 2ab + b² to find 64².
31. 31.Use (a + b)(a − b) = a² − b² to find 61 × 59.
32. 32.Use (a − b)² = a² − 2ab + b² to find 85².
33. 33.Use (a − b)² = a² − 2ab + b² to find 96².
34. 34.Use (a − b)² = a² − 2ab + b² to find 92².
35. 35.Use a² − b² = (a + b)(a − b) to find 67² − 41².
36. 36.Find the value of x² − 2xy + y² when x = 4 and y = 1.
37. 37.Use (a + b)² = a² + 2ab + b² to find 46².
38. 38.Use (a − b)² = a² − 2ab + b² to find 49².
39. 39.Use (a + b)² = a² + 2ab + b² to find 58².
40. 40.Find the value of x² − 2xy + y² when x = 13 and y = 1.

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