Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 916 · 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 a² − b² = (a + b)(a − b) to find 98² − 77².
2. 2.Use (a + b)² = a² + 2ab + b² to find 33².
3. 3.If a + b = 10 and ab = 21, what is a² + b²?
4. 4.Use (a + b)² = a² + 2ab + b² to find 58².
5. 5.Use (a + b)(a − b) = a² − b² to find 76 × 64.
6. 6.Use (a + b)(a − b) = a² − b² to find 71 × 69.
7. 7.Use a² − b² = (a + b)(a − b) to find 49² − 2².
8. 8.Use (a − b)² = a² − 2ab + b² to find 55².
9. 9.Use (a − b)² = a² − 2ab + b² to find 28².
10. 10.Use (a + b)² = a² + 2ab + b² to find 63².
11. 11.Use (a + b)² = a² + 2ab + b² to find 31².
12. 12.Use (a − b)² = a² − 2ab + b² to find 78².
13. 13.Find the value of x² − y² when x = 4 and y = 1.
14. 14.If a + b = 4 and ab = 3, what is a² + b²?
15. 15.Use (a + b)² = a² + 2ab + b² to find 18².
16. 16.Use (a − b)² = a² − 2ab + b² to find 87².
17. 17.Use (a − b)² = a² − 2ab + b² to find 12².
18. 18.Use a² − b² = (a + b)(a − b) to find 70² − 8².
19. 19.Use (a + b)² = a² + 2ab + b² to find 72².
20. 20.If a + b = 13 and ab = 42, what is a² + b²?
21. 21.Use (a + b)(a − b) = a² − b² to find 53 × 47.
22. 22.If a + b = 6 and ab = 5, what is a² + b²?
23. 23.Use (a + b)(a − b) = a² − b² to find 25 × 15.
24. 24.Find the value of x² − 2xy + y² when x = 5 and y = 4.
25. 25.Use a² − b² = (a + b)(a − b) to find 86² − 15².
26. 26.Use (a − b)² = a² − 2ab + b² to find 75².
27. 27.If a + b = 14 and ab = 33, what is a² + b²?
28. 28.Use (a − b)² = a² − 2ab + b² to find 44².
29. 29.Use a² − b² = (a + b)(a − b) to find 86² − 60².
30. 30.Use (a + b)(a − b) = a² − b² to find 48 × 32.
31. 31.Find the value of x² − y² when x = 11 and y = 9.
32. 32.Use (a + b)² = a² + 2ab + b² to find 32².
33. 33.If a − b = 7 and ab = 8, what is a² + b²?
34. 34.Use a² − b² = (a + b)(a − b) to find 48² − 2².
35. 35.If a + b = 7 and ab = 6, what is a² + b²?
36. 36.If a + b = 3 and ab = 2, what is a² + b²?
37. 37.If a − b = 2 and ab = 8, what is a² + b²?
38. 38.Use (a − b)² = a² − 2ab + b² to find 42².
39. 39.Use (a − b)² = a² − 2ab + b² to find 23².
40. 40.If a − b = 4 and ab = 5, what is a² + b²?

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