Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 677 · 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 = 4 and ab = 77, what is a² + b²?
2. 2.If a − b = 2 and ab = 63, what is a² + b²?
3. 3.Use (a − b)² = a² − 2ab + b² to find 55².
4. 4.If a − b = 7 and ab = 18, what is a² + b²?
5. 5.Use (a + b)(a − b) = a² − b² to find 74 × 66.
6. 6.If a + b = 8 and ab = 15, what is a² + b²?
7. 7.Use (a + b)² = a² + 2ab + b² to find 27².
8. 8.Use a² − b² = (a + b)(a − b) to find 39² − 23².
9. 9.Use (a + b)² = a² + 2ab + b² to find 77².
10. 10.Use (a − b)² = a² − 2ab + b² to find 59².
11. 11.Use (a + b)² = a² + 2ab + b² to find 18².
12. 12.Find the value of x² + 2xy + y² when x = 11 and y = 7.
13. 13.Use (a + b)(a − b) = a² − b² to find 64 × 56.
14. 14.Use a² − b² = (a + b)(a − b) to find 46² − 37².
15. 15.Use a² − b² = (a + b)(a − b) to find 99² − 9².
16. 16.Find the value of x² − y² when x = 6 and y = 3.
17. 17.Find the value of x² + 2xy + y² when x = 11 and y = 3.
18. 18.Find the value of x² − 2xy + y² when x = 11 and y = 10.
19. 19.Find the value of x² − y² when x = 4 and y = 3.
20. 20.Use a² − b² = (a + b)(a − b) to find 79² − 7².
21. 21.Use (a + b)² = a² + 2ab + b² to find 34².
22. 22.Use (a − b)² = a² − 2ab + b² to find 79².
23. 23.Use (a + b)² = a² + 2ab + b² to find 15².
24. 24.Use (a + b)² = a² + 2ab + b² to find 79².
25. 25.Use (a + b)² = a² + 2ab + b² to find 101².
26. 26.Use (a + b)² = a² + 2ab + b² to find 31².
27. 27.Find the value of x² − 2xy + y² when x = 15 and y = 13.
28. 28.Use (a − b)² = a² − 2ab + b² to find 49².
29. 29.Use (a + b)² = a² + 2ab + b² to find 92².
30. 30.Use a² − b² = (a + b)(a − b) to find 52² − 27².
31. 31.Find the value of x² − y² when x = 3 and y = 1.
32. 32.Find the value of x² + 2xy + y² when x = 15 and y = 14.
33. 33.Use (a + b)² = a² + 2ab + b² to find 26².
34. 34.Use (a − b)² = a² − 2ab + b² to find 13².
35. 35.If a − b = 9 and ab = 22, what is a² + b²?
36. 36.Use (a + b)(a − b) = a² − b² to find 44 × 36.
37. 37.Find the value of x² − 2xy + y² when x = 7 and y = 3.
38. 38.Use (a − b)² = a² − 2ab + b² to find 92².
39. 39.Use (a + b)(a − b) = a² − b² to find 47 × 33.
40. 40.Use (a + b)(a − b) = a² − b² to find 48 × 32.

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