Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 179 · 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 33².
2. 2.Use (a + b)² = a² + 2ab + b² to find 51².
3. 3.Find the value of x² − y² when x = 14 and y = 10.
4. 4.Use (a + b)² = a² + 2ab + b² to find 65².
5. 5.Use a² − b² = (a + b)(a − b) to find 31² − 20².
6. 6.If a + b = 6 and ab = 5, what is a² + b²?
7. 7.Use a² − b² = (a + b)(a − b) to find 49² − 47².
8. 8.Find the value of x² − 2xy + y² when x = 3 and y = 2.
9. 9.Use (a + b)² = a² + 2ab + b² to find 32².
10. 10.If a + b = 19 and ab = 84, what is a² + b²?
11. 11.Use a² − b² = (a + b)(a − b) to find 46² − 4².
12. 12.Use (a + b)² = a² + 2ab + b² to find 53².
13. 13.Use (a − b)² = a² − 2ab + b² to find 15².
14. 14.Find the value of x² − 2xy + y² when x = 14 and y = 3.
15. 15.If a − b = 3 and ab = 88, what is a² + b²?
16. 16.Use a² − b² = (a + b)(a − b) to find 35² − 1².
17. 17.Find the value of x² − 2xy + y² when x = 7 and y = 2.
18. 18.Use (a − b)² = a² − 2ab + b² to find 99².
19. 19.Use (a − b)² = a² − 2ab + b² to find 69².
20. 20.Use (a − b)² = a² − 2ab + b² to find 53².
21. 21.Use (a + b)² = a² + 2ab + b² to find 22².
22. 22.If a + b = 16 and ab = 55, what is a² + b²?
23. 23.Use a² − b² = (a + b)(a − b) to find 29² − 23².
24. 24.Use (a − b)² = a² − 2ab + b² to find 67².
25. 25.Find the value of x² − 2xy + y² when x = 13 and y = 1.
26. 26.Use a² − b² = (a + b)(a − b) to find 79² − 17².
27. 27.Use (a + b)² = a² + 2ab + b² to find 31².
28. 28.Find the value of x² − y² when x = 14 and y = 7.
29. 29.Use (a + b)² = a² + 2ab + b² to find 23².
30. 30.Use (a − b)² = a² − 2ab + b² to find 72².
31. 31.If a − b = 2 and ab = 3, what is a² + b²?
32. 32.Use (a − b)² = a² − 2ab + b² to find 25².
33. 33.Use a² − b² = (a + b)(a − b) to find 52² − 51².
34. 34.If a + b = 5 and ab = 6, what is a² + b²?
35. 35.Find the value of x² − 2xy + y² when x = 6 and y = 1.
36. 36.Use a² − b² = (a + b)(a − b) to find 85² − 34².
37. 37.If a + b = 12 and ab = 27, what is a² + b²?
38. 38.If a − b = 2 and ab = 15, what is a² + b²?
39. 39.Use (a + b)² = a² + 2ab + b² to find 73².
40. 40.If a + b = 11 and ab = 30, what is a² + b²?

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