Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 838 · 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.Find the value of x² − 2xy + y² when x = 15 and y = 14.
2. 2.Use (a + b)² = a² + 2ab + b² to find 32².
3. 3.Find the value of x² − 2xy + y² when x = 9 and y = 5.
4. 4.Use (a + b)(a − b) = a² − b² to find 56 × 44.
5. 5.Use a² − b² = (a + b)(a − b) to find 47² − 19².
6. 6.Find the value of x² − 2xy + y² when x = 14 and y = 9.
7. 7.If a − b = 2 and ab = 8, what is a² + b²?
8. 8.Use (a + b)² = a² + 2ab + b² to find 35².
9. 9.Use a² − b² = (a + b)(a − b) to find 39² − 7².
10. 10.Use (a + b)(a − b) = a² − b² to find 76 × 64.
11. 11.Use (a + b)² = a² + 2ab + b² to find 38².
12. 12.Use (a + b)(a − b) = a² − b² to find 43 × 37.
13. 13.Use a² − b² = (a + b)(a − b) to find 93² − 2².
14. 14.Use (a + b)² = a² + 2ab + b² to find 95².
15. 15.If a + b = 7 and ab = 12, what is a² + b²?
16. 16.Use (a + b)² = a² + 2ab + b² to find 13².
17. 17.Use a² − b² = (a + b)(a − b) to find 31² − 21².
18. 18.Use (a + b)(a − b) = a² − b² to find 41 × 39.
19. 19.Find the value of x² + 2xy + y² when x = 9 and y = 5.
20. 20.Find the value of x² − y² when x = 3 and y = 1.
21. 21.Use a² − b² = (a + b)(a − b) to find 94² − 54².
22. 22.Find the value of x² − y² when x = 10 and y = 5.
23. 23.Use (a − b)² = a² − 2ab + b² to find 72².
24. 24.If a + b = 14 and ab = 45, what is a² + b²?
25. 25.Find the value of x² + 2xy + y² when x = 9 and y = 4.
26. 26.Use (a + b)(a − b) = a² − b² to find 83 × 77.
27. 27.Use (a + b)² = a² + 2ab + b² to find 33².
28. 28.Use (a + b)² = a² + 2ab + b² to find 36².
29. 29.Use (a + b)² = a² + 2ab + b² to find 19².
30. 30.If a − b = 1 and ab = 2, what is a² + b²?
31. 31.Use (a − b)² = a² − 2ab + b² to find 89².
32. 32.Use (a + b)² = a² + 2ab + b² to find 103².
33. 33.Use (a + b)² = a² + 2ab + b² to find 12².
34. 34.Use (a + b)(a − b) = a² − b² to find 38 × 22.
35. 35.If a + b = 17 and ab = 60, what is a² + b²?
36. 36.Use (a − b)² = a² − 2ab + b² to find 91².
37. 37.Use (a + b)² = a² + 2ab + b² to find 34².
38. 38.Use (a + b)² = a² + 2ab + b² to find 49².
39. 39.Use (a − b)² = a² − 2ab + b² to find 68².
40. 40.Use (a − b)² = a² − 2ab + b² to find 16².

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