Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 908 · 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 a² − b² = (a + b)(a − b) to find 72² − 17².
2. 2.Find the value of x² + 2xy + y² when x = 3 and y = 2.
3. 3.If a + b = 14 and ab = 40, what is a² + b²?
4. 4.Use a² − b² = (a + b)(a − b) to find 74² − 14².
5. 5.Use a² − b² = (a + b)(a − b) to find 27² − 1².
6. 6.Use (a + b)(a − b) = a² − b² to find 38 × 22.
7. 7.Find the value of x² + 2xy + y² when x = 15 and y = 2.
8. 8.Use (a + b)² = a² + 2ab + b² to find 74².
9. 9.Use (a + b)² = a² + 2ab + b² to find 16².
10. 10.If a − b = 1 and ab = 30, what is a² + b²?
11. 11.Find the value of x² − y² when x = 4 and y = 2.
12. 12.Use (a + b)² = a² + 2ab + b² to find 11².
13. 13.Find the value of x² − y² when x = 5 and y = 2.
14. 14.Use (a + b)² = a² + 2ab + b² to find 44².
15. 15.Use (a − b)² = a² − 2ab + b² to find 52².
16. 16.Use (a − b)² = a² − 2ab + b² to find 48².
17. 17.Use (a − b)² = a² − 2ab + b² to find 21².
18. 18.Find the value of x² + 2xy + y² when x = 4 and y = 3.
19. 19.Use (a − b)² = a² − 2ab + b² to find 39².
20. 20.Use (a − b)² = a² − 2ab + b² to find 76².
21. 21.Use (a − b)² = a² − 2ab + b² to find 53².
22. 22.If a + b = 4 and ab = 3, what is a² + b²?
23. 23.If a + b = 5 and ab = 6, what is a² + b²?
24. 24.Find the value of x² − y² when x = 9 and y = 7.
25. 25.Use (a + b)(a − b) = a² − b² to find 82 × 78.
26. 26.Use (a + b)(a − b) = a² − b² to find 24 × 16.
27. 27.Use (a − b)² = a² − 2ab + b² to find 37².
28. 28.Use (a + b)(a − b) = a² − b² to find 29 × 11.
29. 29.Find the value of x² − 2xy + y² when x = 3 and y = 2.
30. 30.If a − b = 2 and ab = 8, what is a² + b²?
31. 31.Use (a − b)² = a² − 2ab + b² to find 66².
32. 32.Find the value of x² + 2xy + y² when x = 11 and y = 10.
33. 33.Use (a + b)² = a² + 2ab + b² to find 32².
34. 34.Find the value of x² − 2xy + y² when x = 10 and y = 3.
35. 35.Use (a + b)(a − b) = a² − b² to find 98 × 82.
36. 36.Use (a + b)(a − b) = a² − b² to find 62 × 58.
37. 37.If a + b = 14 and ab = 48, what is a² + b²?
38. 38.Use (a + b)² = a² + 2ab + b² to find 75².
39. 39.Use (a + b)(a − b) = a² − b² to find 37 × 23.
40. 40.Find the value of x² − y² when x = 3 and y = 2.

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