Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 499 · 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)² = a² − 2ab + b² to find 45².
2. 2.Use a² − b² = (a + b)(a − b) to find 85² − 76².
3. 3.Use (a + b)² = a² + 2ab + b² to find 21².
4. 4.If a + b = 7 and ab = 10, what is a² + b²?
5. 5.Find the value of x² − 2xy + y² when x = 8 and y = 7.
6. 6.Use (a + b)(a − b) = a² − b² to find 86 × 74.
7. 7.Use (a − b)² = a² − 2ab + b² to find 41².
8. 8.Use (a + b)² = a² + 2ab + b² to find 15².
9. 9.Find the value of x² − y² when x = 8 and y = 3.
10. 10.Find the value of x² − y² when x = 4 and y = 3.
11. 11.Find the value of x² − y² when x = 9 and y = 1.
12. 12.Use (a + b)² = a² + 2ab + b² to find 12².
13. 13.Use a² − b² = (a + b)(a − b) to find 74² − 68².
14. 14.Use (a − b)² = a² − 2ab + b² to find 44².
15. 15.If a − b = 1 and ab = 132, what is a² + b²?
16. 16.Use (a − b)² = a² − 2ab + b² to find 47².
17. 17.If a − b = 5 and ab = 24, what is a² + b²?
18. 18.Find the value of x² + 2xy + y² when x = 3 and y = 1.
19. 19.Use a² − b² = (a + b)(a − b) to find 47² − 12².
20. 20.Find the value of x² + 2xy + y² when x = 10 and y = 8.
21. 21.Use (a + b)(a − b) = a² − b² to find 109 × 91.
22. 22.Use a² − b² = (a + b)(a − b) to find 32² − 23².
23. 23.Find the value of x² + 2xy + y² when x = 5 and y = 1.
24. 24.Use (a + b)² = a² + 2ab + b² to find 54².
25. 25.Use (a − b)² = a² − 2ab + b² to find 38².
26. 26.Use (a − b)² = a² − 2ab + b² to find 83².
27. 27.If a + b = 12 and ab = 35, what is a² + b²?
28. 28.If a + b = 5 and ab = 6, what is a² + b²?
29. 29.Find the value of x² + 2xy + y² when x = 15 and y = 9.
30. 30.Use (a + b)² = a² + 2ab + b² to find 66².
31. 31.If a + b = 10 and ab = 24, what is a² + b²?
32. 32.Use (a + b)(a − b) = a² − b² to find 27 × 13.
33. 33.Find the value of x² − y² when x = 6 and y = 5.
34. 34.If a + b = 17 and ab = 60, what is a² + b²?
35. 35.If a − b = 1 and ab = 2, what is a² + b²?
36. 36.If a + b = 18 and ab = 72, what is a² + b²?
37. 37.Use a² − b² = (a + b)(a − b) to find 27² − 1².
38. 38.If a + b = 6 and ab = 8, what is a² + b²?
39. 39.Use (a − b)² = a² − 2ab + b² to find 91².
40. 40.Use (a − b)² = a² − 2ab + b² to find 31².

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