Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 102 · 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 33² − 6².
2. 2.Use (a + b)(a − b) = a² − b² to find 58 × 42.
3. 3.Use a² − b² = (a + b)(a − b) to find 47² − 26².
4. 4.If a + b = 9 and ab = 20, what is a² + b²?
5. 5.Use a² − b² = (a + b)(a − b) to find 90² − 22².
6. 6.Use (a + b)² = a² + 2ab + b² to find 53².
7. 7.Use (a − b)² = a² − 2ab + b² to find 69².
8. 8.If a + b = 3 and ab = 2, what is a² + b²?
9. 9.Find the value of x² + 2xy + y² when x = 14 and y = 12.
10. 10.Use a² − b² = (a + b)(a − b) to find 66² − 6².
11. 11.Use (a + b)² = a² + 2ab + b² to find 106².
12. 12.Use (a + b)² = a² + 2ab + b² to find 28².
13. 13.Find the value of x² − y² when x = 5 and y = 2.
14. 14.Use (a + b)(a − b) = a² − b² to find 82 × 78.
15. 15.Use (a + b)² = a² + 2ab + b² to find 67².
16. 16.Find the value of x² − 2xy + y² when x = 3 and y = 1.
17. 17.Use (a + b)² = a² + 2ab + b² to find 99².
18. 18.Use (a + b)² = a² + 2ab + b² to find 79².
19. 19.Use a² − b² = (a + b)(a − b) to find 43² − 8².
20. 20.Find the value of x² − 2xy + y² when x = 8 and y = 5.
21. 21.If a + b = 19 and ab = 90, what is a² + b²?
22. 22.If a + b = 6 and ab = 8, what is a² + b²?
23. 23.Use (a + b)(a − b) = a² − b² to find 77 × 63.
24. 24.Use (a − b)² = a² − 2ab + b² to find 96².
25. 25.Use a² − b² = (a + b)(a − b) to find 20² − 4².
26. 26.Find the value of x² + 2xy + y² when x = 7 and y = 2.
27. 27.Use a² − b² = (a + b)(a − b) to find 52² − 20².
28. 28.Use (a + b)(a − b) = a² − b² to find 41 × 39.
29. 29.Use (a − b)² = a² − 2ab + b² to find 68².
30. 30.Use (a − b)² = a² − 2ab + b² to find 49².
31. 31.Use a² − b² = (a + b)(a − b) to find 94² − 27².
32. 32.Use (a + b)² = a² + 2ab + b² to find 18².
33. 33.Use a² − b² = (a + b)(a − b) to find 90² − 43².
34. 34.Use (a + b)(a − b) = a² − b² to find 92 × 88.
35. 35.If a − b = 1 and ab = 20, what is a² + b²?
36. 36.Use (a + b)² = a² + 2ab + b² to find 36².
37. 37.Use (a + b)(a − b) = a² − b² to find 85 × 75.
38. 38.If a − b = 4 and ab = 96, what is a² + b²?
39. 39.Use a² − b² = (a + b)(a − b) to find 43² − 10².
40. 40.Use (a + b)² = a² + 2ab + b² to find 109².

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