Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 456 · 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 88².
2. 2.Find the value of x² + 2xy + y² when x = 8 and y = 3.
3. 3.Use a² − b² = (a + b)(a − b) to find 72² − 33².
4. 4.Use (a + b)(a − b) = a² − b² to find 105 × 95.
5. 5.Use a² − b² = (a + b)(a − b) to find 43² − 7².
6. 6.Use (a + b)(a − b) = a² − b² to find 89 × 71.
7. 7.Use (a + b)(a − b) = a² − b² to find 48 × 32.
8. 8.Use a² − b² = (a + b)(a − b) to find 48² − 16².
9. 9.Use (a − b)² = a² − 2ab + b² to find 71².
10. 10.Use a² − b² = (a + b)(a − b) to find 29² − 19².
11. 11.Use a² − b² = (a + b)(a − b) to find 92² − 20².
12. 12.Use a² − b² = (a + b)(a − b) to find 68² − 14².
13. 13.If a − b = 2 and ab = 80, what is a² + b²?
14. 14.Use (a + b)(a − b) = a² − b² to find 39 × 21.
15. 15.Use (a − b)² = a² − 2ab + b² to find 54².
16. 16.If a − b = 7 and ab = 8, what is a² + b²?
17. 17.Use (a + b)² = a² + 2ab + b² to find 63².
18. 18.Use (a + b)² = a² + 2ab + b² to find 37².
19. 19.Use (a + b)² = a² + 2ab + b² to find 23².
20. 20.Find the value of x² − 2xy + y² when x = 10 and y = 9.
21. 21.Use (a + b)² = a² + 2ab + b² to find 79².
22. 22.Use (a − b)² = a² − 2ab + b² to find 96².
23. 23.Use a² − b² = (a + b)(a − b) to find 43² − 10².
24. 24.Use (a + b)(a − b) = a² − b² to find 51 × 49.
25. 25.Use (a − b)² = a² − 2ab + b² to find 75².
26. 26.Use (a + b)² = a² + 2ab + b² to find 18².
27. 27.Use a² − b² = (a + b)(a − b) to find 31² − 6².
28. 28.Use (a + b)² = a² + 2ab + b² to find 97².
29. 29.Use (a + b)(a − b) = a² − b² to find 99 × 81.
30. 30.Use a² − b² = (a + b)(a − b) to find 84² − 67².
31. 31.Use (a + b)² = a² + 2ab + b² to find 31².
32. 32.Use a² − b² = (a + b)(a − b) to find 65² − 47².
33. 33.If a + b = 11 and ab = 10, what is a² + b²?
34. 34.Use a² − b² = (a + b)(a − b) to find 51² − 42².
35. 35.Find the value of x² + 2xy + y² when x = 6 and y = 2.
36. 36.If a − b = 6 and ab = 16, what is a² + b²?
37. 37.Use (a + b)(a − b) = a² − b² to find 44 × 36.
38. 38.Use a² − b² = (a + b)(a − b) to find 30² − 22².
39. 39.Use (a − b)² = a² − 2ab + b² to find 32².
40. 40.Use a² − b² = (a + b)(a − b) to find 87² − 2².

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