Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 761 · 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 48².
2. 2.Use a² − b² = (a + b)(a − b) to find 96² − 75².
3. 3.Use (a + b)(a − b) = a² − b² to find 69 × 51.
4. 4.Use a² − b² = (a + b)(a − b) to find 30² − 28².
5. 5.Find the value of x² + 2xy + y² when x = 6 and y = 3.
6. 6.Find the value of x² − y² when x = 10 and y = 4.
7. 7.If a − b = 1 and ab = 110, what is a² + b²?
8. 8.Use a² − b² = (a + b)(a − b) to find 69² − 49².
9. 9.Use (a + b)(a − b) = a² − b² to find 29 × 11.
10. 10.Use (a + b)(a − b) = a² − b² to find 46 × 34.
11. 11.Use a² − b² = (a + b)(a − b) to find 33² − 30².
12. 12.Find the value of x² + 2xy + y² when x = 13 and y = 12.
13. 13.Find the value of x² − y² when x = 12 and y = 4.
14. 14.If a + b = 18 and ab = 77, what is a² + b²?
15. 15.Use (a + b)² = a² + 2ab + b² to find 92².
16. 16.Use (a + b)² = a² + 2ab + b² to find 69².
17. 17.Use a² − b² = (a + b)(a − b) to find 62² − 42².
18. 18.Use a² − b² = (a + b)(a − b) to find 95² − 89².
19. 19.Use (a − b)² = a² − 2ab + b² to find 25².
20. 20.Use (a − b)² = a² − 2ab + b² to find 14².
21. 21.If a + b = 15 and ab = 50, what is a² + b²?
22. 22.Use (a + b)(a − b) = a² − b² to find 31 × 29.
23. 23.Use (a + b)(a − b) = a² − b² to find 33 × 27.
24. 24.Use (a + b)(a − b) = a² − b² to find 97 × 83.
25. 25.Find the value of x² − y² when x = 15 and y = 8.
26. 26.If a + b = 17 and ab = 66, what is a² + b²?
27. 27.Find the value of x² − y² when x = 5 and y = 4.
28. 28.Find the value of x² − 2xy + y² when x = 9 and y = 1.
29. 29.Use (a − b)² = a² − 2ab + b² to find 43².
30. 30.Use a² − b² = (a + b)(a − b) to find 84² − 26².
31. 31.Use (a + b)² = a² + 2ab + b² to find 72².
32. 32.Use a² − b² = (a + b)(a − b) to find 20² − 2².
33. 33.If a + b = 7 and ab = 12, what is a² + b²?
34. 34.Use (a + b)² = a² + 2ab + b² to find 55².
35. 35.Use a² − b² = (a + b)(a − b) to find 46² − 31².
36. 36.Use (a − b)² = a² − 2ab + b² to find 73².
37. 37.Use (a + b)² = a² + 2ab + b² to find 46².
38. 38.Use (a − b)² = a² − 2ab + b² to find 41².
39. 39.Use (a + b)(a − b) = a² − b² to find 27 × 13.
40. 40.Use a² − b² = (a + b)(a − b) to find 40² − 32².

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