Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 262 · 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 − y² when x = 3 and y = 1.
2. 2.Use (a − b)² = a² − 2ab + b² to find 86².
3. 3.Use (a − b)² = a² − 2ab + b² to find 11².
4. 4.Find the value of x² − 2xy + y² when x = 5 and y = 1.
5. 5.Use (a + b)² = a² + 2ab + b² to find 28².
6. 6.Use (a + b)² = a² + 2ab + b² to find 74².
7. 7.Use a² − b² = (a + b)(a − b) to find 35² − 25².
8. 8.If a + b = 13 and ab = 12, what is a² + b²?
9. 9.Use (a + b)² = a² + 2ab + b² to find 31².
10. 10.Use a² − b² = (a + b)(a − b) to find 30² − 25².
11. 11.Use (a + b)² = a² + 2ab + b² to find 53².
12. 12.Use (a − b)² = a² − 2ab + b² to find 45².
13. 13.Use (a + b)² = a² + 2ab + b² to find 64².
14. 14.Use (a + b)(a − b) = a² − b² to find 83 × 77.
15. 15.Find the value of x² − 2xy + y² when x = 10 and y = 8.
16. 16.Find the value of x² − y² when x = 8 and y = 6.
17. 17.Use (a − b)² = a² − 2ab + b² to find 52².
18. 18.Use (a + b)(a − b) = a² − b² to find 79 × 61.
19. 19.Use (a + b)(a − b) = a² − b² to find 91 × 89.
20. 20.Find the value of x² + 2xy + y² when x = 11 and y = 2.
21. 21.If a − b = 4 and ab = 96, what is a² + b²?
22. 22.Use a² − b² = (a + b)(a − b) to find 87² − 14².
23. 23.Use a² − b² = (a + b)(a − b) to find 39² − 1².
24. 24.Use a² − b² = (a + b)(a − b) to find 84² − 54².
25. 25.Find the value of x² − y² when x = 11 and y = 1.
26. 26.If a − b = 1 and ab = 6, what is a² + b²?
27. 27.Use (a + b)² = a² + 2ab + b² to find 101².
28. 28.Use (a + b)(a − b) = a² − b² to find 63 × 57.
29. 29.Use (a − b)² = a² − 2ab + b² to find 38².
30. 30.Use (a + b)² = a² + 2ab + b² to find 88².
31. 31.Use a² − b² = (a + b)(a − b) to find 37² − 33².
32. 32.Use (a + b)(a − b) = a² − b² to find 72 × 68.
33. 33.Use a² − b² = (a + b)(a − b) to find 71² − 35².
34. 34.Find the value of x² + 2xy + y² when x = 3 and y = 2.
35. 35.Find the value of x² − y² when x = 10 and y = 4.
36. 36.Use (a + b)² = a² + 2ab + b² to find 99².
37. 37.Use a² − b² = (a + b)(a − b) to find 51² − 22².
38. 38.Use (a − b)² = a² − 2ab + b² to find 43².
39. 39.Use (a − b)² = a² − 2ab + b² to find 68².
40. 40.Use (a + b)² = a² + 2ab + b² to find 17².

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