Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 823 · 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 = 7 and ab = 6, what is a² + b²?
2. 2.If a + b = 7 and ab = 12, what is a² + b²?
3. 3.Use (a + b)(a − b) = a² − b² to find 44 × 36.
4. 4.Find the value of x² − 2xy + y² when x = 11 and y = 2.
5. 5.Use (a + b)(a − b) = a² − b² to find 71 × 69.
6. 6.Use (a + b)² = a² + 2ab + b² to find 96².
7. 7.Use (a + b)(a − b) = a² − b² to find 57 × 43.
8. 8.Use a² − b² = (a + b)(a − b) to find 77² − 44².
9. 9.Find the value of x² − y² when x = 11 and y = 3.
10. 10.If a + b = 3 and ab = 2, what is a² + b²?
11. 11.Use (a + b)(a − b) = a² − b² to find 25 × 15.
12. 12.Use a² − b² = (a + b)(a − b) to find 48² − 26².
13. 13.Use a² − b² = (a + b)(a − b) to find 65² − 34².
14. 14.If a − b = 1 and ab = 30, what is a² + b²?
15. 15.Use (a + b)² = a² + 2ab + b² to find 75².
16. 16.Use a² − b² = (a + b)(a − b) to find 64² − 61².
17. 17.Use (a − b)² = a² − 2ab + b² to find 32².
18. 18.Use a² − b² = (a + b)(a − b) to find 48² − 34².
19. 19.Use a² − b² = (a + b)(a − b) to find 99² − 25².
20. 20.If a − b = 2 and ab = 48, what is a² + b²?
21. 21.Use (a + b)(a − b) = a² − b² to find 23 × 17.
22. 22.Use a² − b² = (a + b)(a − b) to find 78² − 33².
23. 23.Use (a + b)² = a² + 2ab + b² to find 69².
24. 24.Find the value of x² + 2xy + y² when x = 3 and y = 1.
25. 25.Use a² − b² = (a + b)(a − b) to find 99² − 46².
26. 26.Use a² − b² = (a + b)(a − b) to find 89² − 10².
27. 27.Use (a + b)(a − b) = a² − b² to find 79 × 61.
28. 28.Use a² − b² = (a + b)(a − b) to find 57² − 17².
29. 29.Find the value of x² + 2xy + y² when x = 8 and y = 1.
30. 30.Use (a + b)(a − b) = a² − b² to find 72 × 68.
31. 31.Use (a − b)² = a² − 2ab + b² to find 76².
32. 32.Use (a − b)² = a² − 2ab + b² to find 52².
33. 33.Use (a − b)² = a² − 2ab + b² to find 87².
34. 34.If a + b = 18 and ab = 80, what is a² + b²?
35. 35.Use (a − b)² = a² − 2ab + b² to find 54².
36. 36.Find the value of x² + 2xy + y² when x = 7 and y = 5.
37. 37.If a − b = 1 and ab = 72, what is a² + b²?
38. 38.Use (a − b)² = a² − 2ab + b² to find 27².
39. 39.Use (a + b)² = a² + 2ab + b² to find 73².
40. 40.Use a² − b² = (a + b)(a − b) to find 49² − 36².

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