Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 361 · 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 (a + b)(a − b) = a² − b² to find 106 × 94.
2. 2.If a + b = 6 and ab = 8, what is a² + b²?
3. 3.If a − b = 2 and ab = 24, what is a² + b²?
4. 4.If a − b = 1 and ab = 2, what is a² + b²?
5. 5.Use a² − b² = (a + b)(a − b) to find 94² − 14².
6. 6.Use (a + b)² = a² + 2ab + b² to find 15².
7. 7.Use a² − b² = (a + b)(a − b) to find 39² − 23².
8. 8.Find the value of x² − y² when x = 7 and y = 6.
9. 9.Find the value of x² + 2xy + y² when x = 6 and y = 3.
10. 10.Use a² − b² = (a + b)(a − b) to find 90² − 5².
11. 11.Use (a − b)² = a² − 2ab + b² to find 76².
12. 12.Use a² − b² = (a + b)(a − b) to find 82² − 10².
13. 13.If a − b = 2 and ab = 8, what is a² + b²?
14. 14.Use a² − b² = (a + b)(a − b) to find 28² − 11².
15. 15.Find the value of x² − 2xy + y² when x = 15 and y = 12.
16. 16.Use (a + b)² = a² + 2ab + b² to find 39².
17. 17.Use (a − b)² = a² − 2ab + b² to find 57².
18. 18.Use (a + b)(a − b) = a² − b² to find 63 × 57.
19. 19.Use (a − b)² = a² − 2ab + b² to find 36².
20. 20.Use (a + b)(a − b) = a² − b² to find 46 × 34.
21. 21.Use (a + b)² = a² + 2ab + b² to find 91².
22. 22.Use (a − b)² = a² − 2ab + b² to find 66².
23. 23.Use (a − b)² = a² − 2ab + b² to find 69².
24. 24.Use (a − b)² = a² − 2ab + b² to find 68².
25. 25.Use a² − b² = (a + b)(a − b) to find 38² − 15².
26. 26.Use a² − b² = (a + b)(a − b) to find 92² − 36².
27. 27.Find the value of x² + 2xy + y² when x = 14 and y = 4.
28. 28.Use (a − b)² = a² − 2ab + b² to find 47².
29. 29.Use (a + b)² = a² + 2ab + b² to find 84².
30. 30.Use (a + b)² = a² + 2ab + b² to find 43².
31. 31.Use (a + b)² = a² + 2ab + b² to find 92².
32. 32.If a − b = 2 and ab = 3, what is a² + b²?
33. 33.Find the value of x² − y² when x = 12 and y = 2.
34. 34.Use a² − b² = (a + b)(a − b) to find 63² − 33².
35. 35.Find the value of x² − 2xy + y² when x = 7 and y = 1.
36. 36.Use (a − b)² = a² − 2ab + b² to find 32².
37. 37.Find the value of x² + 2xy + y² when x = 8 and y = 3.
38. 38.Use a² − b² = (a + b)(a − b) to find 24² − 18².
39. 39.Use (a + b)² = a² + 2ab + b² to find 36².
40. 40.Use (a + b)(a − b) = a² − b² to find 21 × 19.

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