Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 614 · 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 81 × 79.
2. 2.Use (a + b)² = a² + 2ab + b² to find 61².
3. 3.Use (a + b)² = a² + 2ab + b² to find 102².
4. 4.Use (a − b)² = a² − 2ab + b² to find 83².
5. 5.Use a² − b² = (a + b)(a − b) to find 58² − 3².
6. 6.Use (a + b)² = a² + 2ab + b² to find 19².
7. 7.Use (a + b)(a − b) = a² − b² to find 62 × 58.
8. 8.Use (a − b)² = a² − 2ab + b² to find 71².
9. 9.Use (a + b)² = a² + 2ab + b² to find 89².
10. 10.Use (a + b)² = a² + 2ab + b² to find 104².
11. 11.Use (a + b)² = a² + 2ab + b² to find 31².
12. 12.Use (a + b)² = a² + 2ab + b² to find 107².
13. 13.Find the value of x² − y² when x = 7 and y = 2.
14. 14.Find the value of x² − 2xy + y² when x = 14 and y = 5.
15. 15.Use (a − b)² = a² − 2ab + b² to find 74².
16. 16.Use (a − b)² = a² − 2ab + b² to find 79².
17. 17.Use (a + b)(a − b) = a² − b² to find 54 × 46.
18. 18.Find the value of x² − y² when x = 14 and y = 3.
19. 19.Use (a + b)(a − b) = a² − b² to find 25 × 15.
20. 20.Use a² − b² = (a + b)(a − b) to find 48² − 10².
21. 21.Use (a + b)(a − b) = a² − b² to find 104 × 96.
22. 22.Find the value of x² + 2xy + y² when x = 12 and y = 9.
23. 23.Find the value of x² + 2xy + y² when x = 14 and y = 6.
24. 24.Use a² − b² = (a + b)(a − b) to find 89² − 85².
25. 25.Use (a − b)² = a² − 2ab + b² to find 12².
26. 26.Use (a + b)² = a² + 2ab + b² to find 41².
27. 27.Use a² − b² = (a + b)(a − b) to find 65² − 29².
28. 28.Use (a + b)(a − b) = a² − b² to find 59 × 41.
29. 29.Find the value of x² − y² when x = 10 and y = 6.
30. 30.Use a² − b² = (a + b)(a − b) to find 35² − 18².
31. 31.Use (a + b)² = a² + 2ab + b² to find 103².
32. 32.Find the value of x² − 2xy + y² when x = 10 and y = 6.
33. 33.Find the value of x² + 2xy + y² when x = 13 and y = 2.
34. 34.If a + b = 5 and ab = 4, what is a² + b²?
35. 35.Find the value of x² − 2xy + y² when x = 6 and y = 5.
36. 36.Use (a − b)² = a² − 2ab + b² to find 86².
37. 37.Find the value of x² + 2xy + y² when x = 7 and y = 4.
38. 38.Use (a + b)² = a² + 2ab + b² to find 71².
39. 39.If a − b = 3 and ab = 10, what is a² + b²?
40. 40.If a + b = 10 and ab = 16, what is a² + b²?

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