Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 492 · 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 35 × 25.
2. 2.Use a² − b² = (a + b)(a − b) to find 50² − 2².
3. 3.If a + b = 5 and ab = 6, what is a² + b²?
4. 4.Find the value of x² + 2xy + y² when x = 3 and y = 1.
5. 5.Use (a + b)² = a² + 2ab + b² to find 45².
6. 6.Find the value of x² − y² when x = 6 and y = 3.
7. 7.Find the value of x² − 2xy + y² when x = 7 and y = 6.
8. 8.Use (a − b)² = a² − 2ab + b² to find 92².
9. 9.If a + b = 3 and ab = 2, what is a² + b²?
10. 10.Use (a − b)² = a² − 2ab + b² to find 99².
11. 11.Find the value of x² − y² when x = 4 and y = 1.
12. 12.Find the value of x² + 2xy + y² when x = 4 and y = 2.
13. 13.Use (a + b)² = a² + 2ab + b² to find 85².
14. 14.Use a² − b² = (a + b)(a − b) to find 27² − 14².
15. 15.Find the value of x² − y² when x = 11 and y = 6.
16. 16.If a − b = 4 and ab = 60, what is a² + b²?
17. 17.Use (a − b)² = a² − 2ab + b² to find 68².
18. 18.If a − b = 10 and ab = 24, what is a² + b²?
19. 19.Use (a − b)² = a² − 2ab + b² to find 72².
20. 20.Use (a − b)² = a² − 2ab + b² to find 74².
21. 21.Use (a + b)(a − b) = a² − b² to find 28 × 12.
22. 22.Use (a + b)(a − b) = a² − b² to find 44 × 36.
23. 23.Use a² − b² = (a + b)(a − b) to find 53² − 18².
24. 24.Use (a + b)² = a² + 2ab + b² to find 89².
25. 25.Use (a + b)² = a² + 2ab + b² to find 104².
26. 26.Use a² − b² = (a + b)(a − b) to find 60² − 42².
27. 27.Use (a + b)(a − b) = a² − b² to find 47 × 33.
28. 28.Use (a + b)(a − b) = a² − b² to find 64 × 56.
29. 29.Use a² − b² = (a + b)(a − b) to find 32² − 13².
30. 30.Use (a + b)² = a² + 2ab + b² to find 64².
31. 31.Use (a + b)(a − b) = a² − b² to find 22 × 18.
32. 32.Use (a + b)² = a² + 2ab + b² to find 77².
33. 33.Use a² − b² = (a + b)(a − b) to find 87² − 64².
34. 34.Use (a + b)² = a² + 2ab + b² to find 49².
35. 35.Use a² − b² = (a + b)(a − b) to find 35² − 23².
36. 36.Use (a + b)(a − b) = a² − b² to find 81 × 79.
37. 37.Use (a + b)(a − b) = a² − b² to find 42 × 38.
38. 38.Use (a − b)² = a² − 2ab + b² to find 76².
39. 39.Use a² − b² = (a + b)(a − b) to find 39² − 22².
40. 40.Use a² − b² = (a + b)(a − b) to find 29² − 26².

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