Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 330 · 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 91 × 89.
2. 2.Use (a + b)(a − b) = a² − b² to find 78 × 62.
3. 3.Find the value of x² − 2xy + y² when x = 8 and y = 5.
4. 4.Use (a + b)² = a² + 2ab + b² to find 22².
5. 5.Use (a − b)² = a² − 2ab + b² to find 92².
6. 6.Use (a + b)(a − b) = a² − b² to find 94 × 86.
7. 7.If a − b = 2 and ab = 48, what is a² + b²?
8. 8.Use (a + b)(a − b) = a² − b² to find 79 × 61.
9. 9.If a − b = 1 and ab = 72, what is a² + b²?
10. 10.If a − b = 1 and ab = 30, what is a² + b²?
11. 11.Use (a + b)(a − b) = a² − b² to find 68 × 52.
12. 12.Use (a + b)² = a² + 2ab + b² to find 16².
13. 13.Use (a + b)(a − b) = a² − b² to find 22 × 18.
14. 14.Use (a − b)² = a² − 2ab + b² to find 25².
15. 15.Find the value of x² − 2xy + y² when x = 4 and y = 3.
16. 16.Use (a + b)² = a² + 2ab + b² to find 73².
17. 17.Use (a − b)² = a² − 2ab + b² to find 43².
18. 18.Use (a + b)(a − b) = a² − b² to find 107 × 93.
19. 19.Find the value of x² − 2xy + y² when x = 13 and y = 10.
20. 20.If a + b = 7 and ab = 12, what is a² + b²?
21. 21.If a + b = 7 and ab = 10, what is a² + b²?
22. 22.Find the value of x² + 2xy + y² when x = 10 and y = 5.
23. 23.Use (a − b)² = a² − 2ab + b² to find 72².
24. 24.Use a² − b² = (a + b)(a − b) to find 20² − 8².
25. 25.Use (a + b)(a − b) = a² − b² to find 73 × 67.
26. 26.Use a² − b² = (a + b)(a − b) to find 22² − 5².
27. 27.Use (a + b)(a − b) = a² − b² to find 36 × 24.
28. 28.Use (a + b)² = a² + 2ab + b² to find 63².
29. 29.Use (a − b)² = a² − 2ab + b² to find 99².
30. 30.If a + b = 12 and ab = 35, 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 83 × 77.
33. 33.Find the value of x² − y² when x = 8 and y = 2.
34. 34.Use (a + b)(a − b) = a² − b² to find 35 × 25.
35. 35.If a + b = 3 and ab = 2, what is a² + b²?
36. 36.Use (a + b)² = a² + 2ab + b² to find 94².
37. 37.Use (a − b)² = a² − 2ab + b² to find 83².
38. 38.If a + b = 23 and ab = 132, what is a² + b²?
39. 39.Use (a + b)² = a² + 2ab + b² to find 108².
40. 40.Use (a + b)² = a² + 2ab + b² to find 85².

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