Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 385 · 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 12².
2. 2.Use a² − b² = (a + b)(a − b) to find 39² − 23².
3. 3.Use (a + b)² = a² + 2ab + b² to find 33².
4. 4.If a + b = 17 and ab = 72, what is a² + b²?
5. 5.Find the value of x² + 2xy + y² when x = 4 and y = 2.
6. 6.Use (a − b)² = a² − 2ab + b² to find 26².
7. 7.If a + b = 5 and ab = 6, what is a² + b²?
8. 8.Use (a + b)(a − b) = a² − b² to find 39 × 21.
9. 9.Use (a + b)² = a² + 2ab + b² to find 21².
10. 10.If a + b = 13 and ab = 36, what is a² + b²?
11. 11.Use (a − b)² = a² − 2ab + b² to find 19².
12. 12.Find the value of x² − 2xy + y² when x = 15 and y = 10.
13. 13.Find the value of x² + 2xy + y² when x = 5 and y = 1.
14. 14.Use (a − b)² = a² − 2ab + b² to find 76².
15. 15.Use (a − b)² = a² − 2ab + b² to find 46².
16. 16.Use (a − b)² = a² − 2ab + b² to find 21².
17. 17.Use (a + b)(a − b) = a² − b² to find 72 × 68.
18. 18.Use (a + b)² = a² + 2ab + b² to find 78².
19. 19.Use (a + b)² = a² + 2ab + b² to find 71².
20. 20.Use (a + b)(a − b) = a² − b² to find 74 × 66.
21. 21.Use (a + b)² = a² + 2ab + b² to find 23².
22. 22.Find the value of x² − y² when x = 4 and y = 1.
23. 23.Use (a − b)² = a² − 2ab + b² to find 74².
24. 24.Use (a + b)² = a² + 2ab + b² to find 103².
25. 25.Use a² − b² = (a + b)(a − b) to find 31² − 7².
26. 26.Find the value of x² − y² when x = 5 and y = 4.
27. 27.Find the value of x² + 2xy + y² when x = 3 and y = 2.
28. 28.Use (a − b)² = a² − 2ab + b² to find 51².
29. 29.Use a² − b² = (a + b)(a − b) to find 71² − 1².
30. 30.Use (a + b)(a − b) = a² − b² to find 56 × 44.
31. 31.Use (a − b)² = a² − 2ab + b² to find 77².
32. 32.If a − b = 1 and ab = 2, what is a² + b²?
33. 33.Use (a − b)² = a² − 2ab + b² to find 94².
34. 34.Use (a + b)² = a² + 2ab + b² to find 98².
35. 35.Use (a + b)² = a² + 2ab + b² to find 89².
36. 36.Find the value of x² − 2xy + y² when x = 7 and y = 3.
37. 37.Use a² − b² = (a + b)(a − b) to find 68² − 18².
38. 38.If a − b = 1 and ab = 12, what is a² + b²?
39. 39.If a + b = 10 and ab = 9, what is a² + b²?
40. 40.Use (a − b)² = a² − 2ab + b² to find 92².

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