Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 30 · 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 29².
2. 2.Use (a − b)² = a² − 2ab + b² to find 56².
3. 3.Use (a − b)² = a² − 2ab + b² to find 73².
4. 4.Use (a + b)(a − b) = a² − b² to find 76 × 64.
5. 5.Use a² − b² = (a + b)(a − b) to find 60² − 22².
6. 6.If a − b = 3 and ab = 54, what is a² + b²?
7. 7.Use a² − b² = (a + b)(a − b) to find 88² − 47².
8. 8.Use (a + b)(a − b) = a² − b² to find 88 × 72.
9. 9.Find the value of x² + 2xy + y² when x = 13 and y = 10.
10. 10.Use a² − b² = (a + b)(a − b) to find 60² − 54².
11. 11.Find the value of x² − 2xy + y² when x = 5 and y = 1.
12. 12.Use (a + b)² = a² + 2ab + b² to find 26².
13. 13.Use (a + b)(a − b) = a² − b² to find 31 × 29.
14. 14.Use (a + b)² = a² + 2ab + b² to find 81².
15. 15.Find the value of x² − 2xy + y² when x = 15 and y = 14.
16. 16.Use (a + b)(a − b) = a² − b² to find 84 × 76.
17. 17.Use (a − b)² = a² − 2ab + b² to find 33².
18. 18.Use (a − b)² = a² − 2ab + b² to find 27².
19. 19.Use (a + b)² = a² + 2ab + b² to find 86².
20. 20.Use (a + b)(a − b) = a² − b² to find 62 × 58.
21. 21.Use (a − b)² = a² − 2ab + b² to find 21².
22. 22.Use (a + b)² = a² + 2ab + b² to find 66².
23. 23.Use a² − b² = (a + b)(a − b) to find 22² − 11².
24. 24.Use (a + b)² = a² + 2ab + b² to find 85².
25. 25.Use a² − b² = (a + b)(a − b) to find 60² − 14².
26. 26.Use (a + b)² = a² + 2ab + b² to find 22².
27. 27.Use (a + b)(a − b) = a² − b² to find 35 × 25.
28. 28.If a − b = 4 and ab = 21, what is a² + b²?
29. 29.Use (a − b)² = a² − 2ab + b² to find 25².
30. 30.Use (a − b)² = a² − 2ab + b² to find 98².
31. 31.Use (a + b)² = a² + 2ab + b² to find 43².
32. 32.Use (a − b)² = a² − 2ab + b² to find 88².
33. 33.If a − b = 2 and ab = 24, what is a² + b²?
34. 34.Use (a − b)² = a² − 2ab + b² to find 99².
35. 35.Find the value of x² − y² when x = 7 and y = 2.
36. 36.Use a² − b² = (a + b)(a − b) to find 60² − 6².
37. 37.Use a² − b² = (a + b)(a − b) to find 30² − 22².
38. 38.Use a² − b² = (a + b)(a − b) to find 62² − 61².
39. 39.If a + b = 11 and ab = 24, what is a² + b²?
40. 40.Use (a − b)² = a² − 2ab + b² to find 44².

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