Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 849 · 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)² = a² + 2ab + b² to find 12².
2. 2.Use (a + b)² = a² + 2ab + b² to find 11².
3. 3.Use (a + b)² = a² + 2ab + b² to find 63².
4. 4.Use (a − b)² = a² − 2ab + b² to find 76².
5. 5.Use a² − b² = (a + b)(a − b) to find 69² − 20².
6. 6.If a + b = 10 and ab = 21, what is a² + b²?
7. 7.Use (a − b)² = a² − 2ab + b² to find 68².
8. 8.Use (a − b)² = a² − 2ab + b² to find 87².
9. 9.Find the value of x² − y² when x = 5 and y = 4.
10. 10.Use (a − b)² = a² − 2ab + b² to find 33².
11. 11.Use (a + b)(a − b) = a² − b² to find 104 × 96.
12. 12.Use (a − b)² = a² − 2ab + b² to find 32².
13. 13.If a − b = 4 and ab = 5, what is a² + b²?
14. 14.Use (a + b)(a − b) = a² − b² to find 55 × 45.
15. 15.Use a² − b² = (a + b)(a − b) to find 32² − 31².
16. 16.Use a² − b² = (a + b)(a − b) to find 48² − 7².
17. 17.Use (a + b)² = a² + 2ab + b² to find 68².
18. 18.Use (a + b)² = a² + 2ab + b² to find 57².
19. 19.Use (a − b)² = a² − 2ab + b² to find 14².
20. 20.Find the value of x² + 2xy + y² when x = 5 and y = 2.
21. 21.Use (a + b)² = a² + 2ab + b² to find 97².
22. 22.Use (a − b)² = a² − 2ab + b² to find 84².
23. 23.Use (a − b)² = a² − 2ab + b² to find 42².
24. 24.Find the value of x² − 2xy + y² when x = 4 and y = 1.
25. 25.Use (a + b)² = a² + 2ab + b² to find 81².
26. 26.Use (a − b)² = a² − 2ab + b² to find 54².
27. 27.Use (a + b)² = a² + 2ab + b² to find 44².
28. 28.Find the value of x² − y² when x = 12 and y = 1.
29. 29.Use (a + b)(a − b) = a² − b² to find 65 × 55.
30. 30.Use (a + b)² = a² + 2ab + b² to find 85².
31. 31.Use (a − b)² = a² − 2ab + b² to find 91².
32. 32.Use (a + b)² = a² + 2ab + b² to find 35².
33. 33.Use a² − b² = (a + b)(a − b) to find 95² − 32².
34. 34.Use (a + b)² = a² + 2ab + b² to find 51².
35. 35.Use (a + b)(a − b) = a² − b² to find 43 × 37.
36. 36.Use a² − b² = (a + b)(a − b) to find 45² − 30².
37. 37.Use a² − b² = (a + b)(a − b) to find 58² − 32².
38. 38.Use a² − b² = (a + b)(a − b) to find 73² − 43².
39. 39.Find the value of x² − y² when x = 14 and y = 10.
40. 40.Find the value of x² + 2xy + y² when x = 4 and y = 2.

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