Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 994 · 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.Find the value of x² − y² when x = 6 and y = 2.
2. 2.If a − b = 1 and ab = 2, what is a² + b²?
3. 3.Use (a + b)(a − b) = a² − b² to find 83 × 77.
4. 4.Use (a − b)² = a² − 2ab + b² to find 69².
5. 5.Use a² − b² = (a + b)(a − b) to find 33² − 32².
6. 6.Use (a − b)² = a² − 2ab + b² to find 18².
7. 7.Use a² − b² = (a + b)(a − b) to find 83² − 63².
8. 8.Use (a + b)(a − b) = a² − b² to find 105 × 95.
9. 9.If a + b = 17 and ab = 60, what is a² + b²?
10. 10.Use (a − b)² = a² − 2ab + b² to find 22².
11. 11.Use (a + b)(a − b) = a² − b² to find 47 × 33.
12. 12.Use a² − b² = (a + b)(a − b) to find 78² − 10².
13. 13.Use (a + b)² = a² + 2ab + b² to find 63².
14. 14.Use (a + b)(a − b) = a² − b² to find 53 × 47.
15. 15.Use (a + b)(a − b) = a² − b² to find 34 × 26.
16. 16.Use (a + b)² = a² + 2ab + b² to find 69².
17. 17.Use a² − b² = (a + b)(a − b) to find 29² − 6².
18. 18.If a − b = 7 and ab = 30, what is a² + b²?
19. 19.Use (a + b)² = a² + 2ab + b² to find 102².
20. 20.Use (a + b)² = a² + 2ab + b² to find 42².
21. 21.If a + b = 3 and ab = 2, what is a² + b²?
22. 22.Use a² − b² = (a + b)(a − b) to find 93² − 42².
23. 23.Use (a + b)² = a² + 2ab + b² to find 109².
24. 24.Use (a + b)(a − b) = a² − b² to find 25 × 15.
25. 25.Find the value of x² − 2xy + y² when x = 3 and y = 2.
26. 26.Find the value of x² − y² when x = 3 and y = 2.
27. 27.Use (a − b)² = a² − 2ab + b² to find 38².
28. 28.Use (a + b)² = a² + 2ab + b² to find 14².
29. 29.Find the value of x² − y² when x = 4 and y = 1.
30. 30.If a + b = 7 and ab = 12, what is a² + b²?
31. 31.Find the value of x² − 2xy + y² when x = 3 and y = 1.
32. 32.Use (a + b)(a − b) = a² − b² to find 85 × 75.
33. 33.If a − b = 2 and ab = 3, what is a² + b²?
34. 34.If a + b = 19 and ab = 90, what is a² + b²?
35. 35.Find the value of x² − y² when x = 5 and y = 1.
36. 36.Find the value of x² − 2xy + y² when x = 10 and y = 5.
37. 37.If a − b = 9 and ab = 22, what is a² + b²?
38. 38.Use (a + b)² = a² + 2ab + b² to find 68².
39. 39.If a + b = 13 and ab = 30, what is a² + b²?
40. 40.Use (a + b)(a − b) = a² − b² to find 43 × 37.

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