Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 269 · 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 20² − 4².
2. 2.Use (a + b)² = a² + 2ab + b² to find 78².
3. 3.Use (a + b)(a − b) = a² − b² to find 107 × 93.
4. 4.Use (a + b)(a − b) = a² − b² to find 98 × 82.
5. 5.Use (a + b)(a − b) = a² − b² to find 31 × 29.
6. 6.Use (a + b)² = a² + 2ab + b² to find 75².
7. 7.Use (a + b)² = a² + 2ab + b² to find 94².
8. 8.Find the value of x² − 2xy + y² when x = 3 and y = 1.
9. 9.Find the value of x² + 2xy + y² when x = 9 and y = 4.
10. 10.Use (a + b)(a − b) = a² − b² to find 43 × 37.
11. 11.Use (a + b)(a − b) = a² − b² to find 72 × 68.
12. 12.Use (a − b)² = a² − 2ab + b² to find 77².
13. 13.If a − b = 3 and ab = 88, what is a² + b²?
14. 14.Use (a − b)² = a² − 2ab + b² to find 45².
15. 15.Use (a − b)² = a² − 2ab + b² to find 41².
16. 16.Use a² − b² = (a + b)(a − b) to find 48² − 16².
17. 17.Use (a − b)² = a² − 2ab + b² to find 71².
18. 18.Use (a + b)(a − b) = a² − b² to find 23 × 17.
19. 19.Use a² − b² = (a + b)(a − b) to find 60² − 25².
20. 20.Use a² − b² = (a + b)(a − b) to find 43² − 35².
21. 21.Find the value of x² − 2xy + y² when x = 13 and y = 2.
22. 22.Use (a − b)² = a² − 2ab + b² to find 88².
23. 23.Find the value of x² − y² when x = 15 and y = 3.
24. 24.Use (a + b)(a − b) = a² − b² to find 47 × 33.
25. 25.Use (a + b)² = a² + 2ab + b² to find 82².
26. 26.Find the value of x² + 2xy + y² when x = 15 and y = 5.
27. 27.Use a² − b² = (a + b)(a − b) to find 24² − 5².
28. 28.Use a² − b² = (a + b)(a − b) to find 34² − 13².
29. 29.Use (a − b)² = a² − 2ab + b² to find 27².
30. 30.Use a² − b² = (a + b)(a − b) to find 54² − 16².
31. 31.Find the value of x² + 2xy + y² when x = 4 and y = 3.
32. 32.If a − b = 5 and ab = 36, what is a² + b²?
33. 33.Use (a − b)² = a² − 2ab + b² to find 75².
34. 34.Use (a − b)² = a² − 2ab + b² to find 24².
35. 35.Use a² − b² = (a + b)(a − b) to find 65² − 41².
36. 36.If a − b = 2 and ab = 8, what is a² + b²?
37. 37.Find the value of x² − y² when x = 4 and y = 1.
38. 38.Use (a + b)(a − b) = a² − b² to find 33 × 27.
39. 39.Find the value of x² + 2xy + y² when x = 11 and y = 4.
40. 40.Use (a + b)(a − b) = a² − b² to find 73 × 67.

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