Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 258 · 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 29².
2. 2.Use (a − b)² = a² − 2ab + b² to find 87².
3. 3.If a − b = 2 and ab = 15, what is a² + b²?
4. 4.Use (a + b)² = a² + 2ab + b² to find 22².
5. 5.Find the value of x² + 2xy + y² when x = 8 and y = 5.
6. 6.Find the value of x² + 2xy + y² when x = 10 and y = 8.
7. 7.Find the value of x² − y² when x = 6 and y = 5.
8. 8.Use (a + b)² = a² + 2ab + b² to find 27².
9. 9.Use (a + b)² = a² + 2ab + b² to find 29².
10. 10.Use (a + b)² = a² + 2ab + b² to find 107².
11. 11.Use a² − b² = (a + b)(a − b) to find 56² − 40².
12. 12.If a − b = 4 and ab = 12, what is a² + b²?
13. 13.Use (a − b)² = a² − 2ab + b² to find 78².
14. 14.Find the value of x² − 2xy + y² when x = 5 and y = 2.
15. 15.Use (a − b)² = a² − 2ab + b² to find 61².
16. 16.Find the value of x² + 2xy + y² when x = 12 and y = 3.
17. 17.Use (a + b)² = a² + 2ab + b² to find 48².
18. 18.If a − b = 5 and ab = 36, what is a² + b²?
19. 19.If a − b = 3 and ab = 70, what is a² + b²?
20. 20.Find the value of x² − y² when x = 4 and y = 1.
21. 21.Use (a + b)(a − b) = a² − b² to find 37 × 23.
22. 22.Find the value of x² + 2xy + y² when x = 6 and y = 3.
23. 23.Use (a − b)² = a² − 2ab + b² to find 27².
24. 24.Find the value of x² − 2xy + y² when x = 7 and y = 3.
25. 25.Use a² − b² = (a + b)(a − b) to find 44² − 17².
26. 26.Find the value of x² − y² when x = 12 and y = 1.
27. 27.If a + b = 10 and ab = 24, what is a² + b²?
28. 28.Find the value of x² + 2xy + y² when x = 8 and y = 4.
29. 29.Use (a + b)(a − b) = a² − b² to find 25 × 15.
30. 30.If a − b = 3 and ab = 18, what is a² + b²?
31. 31.If a + b = 10 and ab = 16, what is a² + b²?
32. 32.If a + b = 5 and ab = 4, what is a² + b²?
33. 33.Use a² − b² = (a + b)(a − b) to find 61² − 26².
34. 34.Use a² − b² = (a + b)(a − b) to find 54² − 13².
35. 35.Use (a + b)² = a² + 2ab + b² to find 84².
36. 36.If a − b = 2 and ab = 3, what is a² + b²?
37. 37.Use (a + b)² = a² + 2ab + b² to find 102².
38. 38.Use a² − b² = (a + b)(a − b) to find 97² − 37².
39. 39.Find the value of x² + 2xy + y² when x = 4 and y = 3.
40. 40.Use (a + b)(a − b) = a² − b² to find 32 × 28.

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