Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 641 · 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 61 × 59.
2. 2.If a − b = 1 and ab = 2, what is a² + b²?
3. 3.Find the value of x² − 2xy + y² when x = 13 and y = 4.
4. 4.Use (a + b)(a − b) = a² − b² to find 21 × 19.
5. 5.Find the value of x² − y² when x = 9 and y = 6.
6. 6.Use a² − b² = (a + b)(a − b) to find 58² − 9².
7. 7.Find the value of x² − y² when x = 6 and y = 4.
8. 8.Use (a − b)² = a² − 2ab + b² to find 96².
9. 9.Use (a + b)² = a² + 2ab + b² to find 29².
10. 10.Use a² − b² = (a + b)(a − b) to find 27² − 15².
11. 11.Use a² − b² = (a + b)(a − b) to find 21² − 5².
12. 12.Use (a + b)² = a² + 2ab + b² to find 79².
13. 13.Find the value of x² − y² when x = 10 and y = 6.
14. 14.Use (a − b)² = a² − 2ab + b² to find 23².
15. 15.Use (a + b)² = a² + 2ab + b² to find 13².
16. 16.Find the value of x² + 2xy + y² when x = 14 and y = 7.
17. 17.Find the value of x² + 2xy + y² when x = 4 and y = 1.
18. 18.If a + b = 11 and ab = 10, what is a² + b²?
19. 19.Use (a + b)(a − b) = a² − b² to find 32 × 28.
20. 20.Use (a − b)² = a² − 2ab + b² to find 49².
21. 21.Use (a − b)² = a² − 2ab + b² to find 31².
22. 22.If a − b = 6 and ab = 27, what is a² + b²?
23. 23.Use a² − b² = (a + b)(a − b) to find 55² − 24².
24. 24.Use (a + b)² = a² + 2ab + b² to find 14².
25. 25.If a + b = 9 and ab = 14, what is a² + b²?
26. 26.Use (a + b)² = a² + 2ab + b² to find 99².
27. 27.Find the value of x² − 2xy + y² when x = 3 and y = 1.
28. 28.Find the value of x² + 2xy + y² when x = 12 and y = 10.
29. 29.Use (a + b)(a − b) = a² − b² to find 91 × 89.
30. 30.Use a² − b² = (a + b)(a − b) to find 35² − 23².
31. 31.Use (a − b)² = a² − 2ab + b² to find 94².
32. 32.Use a² − b² = (a + b)(a − b) to find 39² − 14².
33. 33.If a + b = 18 and ab = 80, what is a² + b²?
34. 34.If a + b = 14 and ab = 24, what is a² + b²?
35. 35.Use (a − b)² = a² − 2ab + b² to find 89².
36. 36.Use a² − b² = (a + b)(a − b) to find 20² − 1².
37. 37.If a + b = 4 and ab = 3, what is a² + b²?
38. 38.Use (a + b)² = a² + 2ab + b² to find 103².
39. 39.Use (a + b)(a − b) = a² − b² to find 52 × 48.
40. 40.Find the value of x² − 2xy + y² when x = 5 and y = 4.

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