Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 326 · 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 33 × 27.
2. 2.If a − b = 1 and ab = 2, what is a² + b²?
3. 3.Use a² − b² = (a + b)(a − b) to find 27² − 1².
4. 4.Use (a − b)² = a² − 2ab + b² to find 59².
5. 5.Use (a + b)² = a² + 2ab + b² to find 32².
6. 6.Use (a − b)² = a² − 2ab + b² to find 35².
7. 7.Use (a − b)² = a² − 2ab + b² to find 39².
8. 8.Find the value of x² − y² when x = 6 and y = 1.
9. 9.Use (a + b)² = a² + 2ab + b² to find 59².
10. 10.Use a² − b² = (a + b)(a − b) to find 28² − 14².
11. 11.Find the value of x² − y² when x = 8 and y = 3.
12. 12.Find the value of x² − 2xy + y² when x = 12 and y = 8.
13. 13.Use (a + b)(a − b) = a² − b² to find 35 × 25.
14. 14.Use (a − b)² = a² − 2ab + b² to find 54².
15. 15.Use (a − b)² = a² − 2ab + b² to find 25².
16. 16.Find the value of x² − y² when x = 15 and y = 3.
17. 17.Use (a − b)² = a² − 2ab + b² to find 17².
18. 18.Use (a + b)(a − b) = a² − b² to find 97 × 83.
19. 19.If a − b = 2 and ab = 3, what is a² + b²?
20. 20.Use a² − b² = (a + b)(a − b) to find 61² − 15².
21. 21.Use (a + b)(a − b) = a² − b² to find 57 × 43.
22. 22.Use (a − b)² = a² − 2ab + b² to find 49².
23. 23.Use (a + b)(a − b) = a² − b² to find 58 × 42.
24. 24.Use a² − b² = (a + b)(a − b) to find 56² − 4².
25. 25.Use (a + b)² = a² + 2ab + b² to find 106².
26. 26.Use (a − b)² = a² − 2ab + b² to find 64².
27. 27.If a + b = 5 and ab = 4, what is a² + b²?
28. 28.Use (a − b)² = a² − 2ab + b² to find 26².
29. 29.If a − b = 3 and ab = 10, what is a² + b²?
30. 30.If a + b = 11 and ab = 18, what is a² + b²?
31. 31.Use (a + b)(a − b) = a² − b² to find 48 × 32.
32. 32.Use (a + b)(a − b) = a² − b² to find 41 × 39.
33. 33.Find the value of x² + 2xy + y² when x = 13 and y = 7.
34. 34.Find the value of x² + 2xy + y² when x = 9 and y = 3.
35. 35.Find the value of x² − y² when x = 6 and y = 3.
36. 36.Use (a + b)(a − b) = a² − b² to find 51 × 49.
37. 37.Use (a + b)(a − b) = a² − b² to find 27 × 13.
38. 38.Use (a + b)² = a² + 2ab + b² to find 51².
39. 39.Use (a + b)² = a² + 2ab + b² to find 61².
40. 40.Use (a − b)² = a² − 2ab + b² to find 55².

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