Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 443 · 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.If a + b = 15 and ab = 36, what is a² + b²?
2. 2.Use (a + b)² = a² + 2ab + b² to find 73².
3. 3.Use (a + b)² = a² + 2ab + b² to find 41².
4. 4.Use a² − b² = (a + b)(a − b) to find 54² − 7².
5. 5.Use (a + b)² = a² + 2ab + b² to find 79².
6. 6.Use (a − b)² = a² − 2ab + b² to find 22².
7. 7.Use (a − b)² = a² − 2ab + b² to find 34².
8. 8.Use (a − b)² = a² − 2ab + b² to find 36².
9. 9.Use (a + b)² = a² + 2ab + b² to find 108².
10. 10.If a + b = 5 and ab = 4, what is a² + b²?
11. 11.Use (a + b)² = a² + 2ab + b² to find 102².
12. 12.Use a² − b² = (a + b)(a − b) to find 69² − 20².
13. 13.Use (a + b)² = a² + 2ab + b² to find 84².
14. 14.Use (a − b)² = a² − 2ab + b² to find 49².
15. 15.Use (a − b)² = a² − 2ab + b² to find 35².
16. 16.Use (a + b)² = a² + 2ab + b² to find 26².
17. 17.Find the value of x² + 2xy + y² when x = 14 and y = 6.
18. 18.Find the value of x² − 2xy + y² when x = 3 and y = 2.
19. 19.Use (a + b)(a − b) = a² − b² to find 51 × 49.
20. 20.Find the value of x² + 2xy + y² when x = 8 and y = 6.
21. 21.Use (a + b)(a − b) = a² − b² to find 33 × 27.
22. 22.If a + b = 22 and ab = 120, what is a² + b²?
23. 23.Use (a + b)(a − b) = a² − b² to find 99 × 81.
24. 24.Use (a + b)² = a² + 2ab + b² to find 54².
25. 25.Find the value of x² − 2xy + y² when x = 10 and y = 8.
26. 26.If a + b = 15 and ab = 54, what is a² + b²?
27. 27.If a − b = 2 and ab = 8, what is a² + b²?
28. 28.Use a² − b² = (a + b)(a − b) to find 33² − 6².
29. 29.Use (a + b)² = a² + 2ab + b² to find 24².
30. 30.Use (a + b)(a − b) = a² − b² to find 62 × 58.
31. 31.Use a² − b² = (a + b)(a − b) to find 88² − 10².
32. 32.Use (a − b)² = a² − 2ab + b² to find 24².
33. 33.Find the value of x² − y² when x = 5 and y = 2.
34. 34.If a − b = 8 and ab = 9, what is a² + b²?
35. 35.Use (a + b)(a − b) = a² − b² to find 75 × 65.
36. 36.If a − b = 1 and ab = 6, what is a² + b²?
37. 37.Find the value of x² − 2xy + y² when x = 7 and y = 1.
38. 38.Use (a − b)² = a² − 2ab + b² to find 65².
39. 39.Use (a + b)² = a² + 2ab + b² to find 36².
40. 40.Find the value of x² − 2xy + y² when x = 11 and y = 3.

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