Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 448 · 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 57².
2. 2.Use a² − b² = (a + b)(a − b) to find 78² − 41².
3. 3.Use a² − b² = (a + b)(a − b) to find 21² − 7².
4. 4.Use (a − b)² = a² − 2ab + b² to find 72².
5. 5.Use (a + b)(a − b) = a² − b² to find 46 × 34.
6. 6.If a − b = 9 and ab = 22, what is a² + b²?
7. 7.Find the value of x² + 2xy + y² when x = 3 and y = 2.
8. 8.Find the value of x² + 2xy + y² when x = 13 and y = 11.
9. 9.Use (a + b)² = a² + 2ab + b² to find 19².
10. 10.If a + b = 6 and ab = 5, what is a² + b²?
11. 11.Use (a + b)(a − b) = a² − b² to find 88 × 72.
12. 12.If a + b = 12 and ab = 11, what is a² + b²?
13. 13.Use (a + b)² = a² + 2ab + b² to find 71².
14. 14.Use (a − b)² = a² − 2ab + b² to find 12².
15. 15.If a + b = 5 and ab = 4, what is a² + b²?
16. 16.Use (a + b)² = a² + 2ab + b² to find 62².
17. 17.Use (a + b)² = a² + 2ab + b² to find 36².
18. 18.Use a² − b² = (a + b)(a − b) to find 58² − 36².
19. 19.Use a² − b² = (a + b)(a − b) to find 35² − 25².
20. 20.Use (a + b)(a − b) = a² − b² to find 52 × 48.
21. 21.Find the value of x² − y² when x = 10 and y = 6.
22. 22.Use (a − b)² = a² − 2ab + b² to find 66².
23. 23.If a − b = 1 and ab = 6, what is a² + b²?
24. 24.Use (a + b)(a − b) = a² − b² to find 22 × 18.
25. 25.Use a² − b² = (a + b)(a − b) to find 74² − 13².
26. 26.Find the value of x² + 2xy + y² when x = 4 and y = 2.
27. 27.Find the value of x² − 2xy + y² when x = 10 and y = 4.
28. 28.Use (a + b)² = a² + 2ab + b² to find 17².
29. 29.Use (a − b)² = a² − 2ab + b² to find 31².
30. 30.Use (a − b)² = a² − 2ab + b² to find 44².
31. 31.Use (a − b)² = a² − 2ab + b² to find 45².
32. 32.Use (a + b)(a − b) = a² − b² to find 41 × 39.
33. 33.Use (a + b)² = a² + 2ab + b² to find 99².
34. 34.Use (a + b)² = a² + 2ab + b² to find 83².
35. 35.Find the value of x² − 2xy + y² when x = 3 and y = 1.
36. 36.Find the value of x² − y² when x = 11 and y = 3.
37. 37.Use (a + b)² = a² + 2ab + b² to find 31².
38. 38.Use a² − b² = (a + b)(a − b) to find 61² − 23².
39. 39.Find the value of x² − y² when x = 8 and y = 4.
40. 40.Find the value of x² − 2xy + y² when x = 11 and y = 5.

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