Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 351 · 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 67 × 53.
2. 2.Use (a − b)² = a² − 2ab + b² to find 35².
3. 3.Use (a − b)² = a² − 2ab + b² to find 18².
4. 4.Use (a + b)(a − b) = a² − b² to find 47 × 33.
5. 5.If a + b = 3 and ab = 2, what is a² + b²?
6. 6.If a − b = 2 and ab = 8, what is a² + b²?
7. 7.If a + b = 4 and ab = 3, what is a² + b²?
8. 8.Find the value of x² − y² when x = 6 and y = 1.
9. 9.Use a² − b² = (a + b)(a − b) to find 54² − 44².
10. 10.Use (a + b)(a − b) = a² − b² to find 44 × 36.
11. 11.Use (a − b)² = a² − 2ab + b² to find 27².
12. 12.Find the value of x² + 2xy + y² when x = 15 and y = 3.
13. 13.Use (a − b)² = a² − 2ab + b² to find 94².
14. 14.Use (a − b)² = a² − 2ab + b² to find 95².
15. 15.Use (a − b)² = a² − 2ab + b² to find 16².
16. 16.Use (a + b)(a − b) = a² − b² to find 32 × 28.
17. 17.Find the value of x² − 2xy + y² when x = 12 and y = 6.
18. 18.Find the value of x² + 2xy + y² when x = 10 and y = 2.
19. 19.Use (a + b)(a − b) = a² − b² to find 63 × 57.
20. 20.Find the value of x² + 2xy + y² when x = 11 and y = 7.
21. 21.If a − b = 1 and ab = 2, what is a² + b²?
22. 22.Use (a − b)² = a² − 2ab + b² to find 57².
23. 23.Use (a − b)² = a² − 2ab + b² to find 45².
24. 24.Use (a + b)² = a² + 2ab + b² to find 33².
25. 25.Use (a − b)² = a² − 2ab + b² to find 11².
26. 26.Use (a − b)² = a² − 2ab + b² to find 39².
27. 27.Use (a + b)(a − b) = a² − b² to find 91 × 89.
28. 28.Use (a + b)² = a² + 2ab + b² to find 102².
29. 29.Use (a + b)² = a² + 2ab + b² to find 14².
30. 30.Use (a + b)(a − b) = a² − b² to find 33 × 27.
31. 31.Use a² − b² = (a + b)(a − b) to find 58² − 16².
32. 32.Use (a + b)(a − b) = a² − b² to find 43 × 37.
33. 33.Use (a + b)(a − b) = a² − b² to find 23 × 17.
34. 34.Use (a + b)² = a² + 2ab + b² to find 74².
35. 35.Use a² − b² = (a + b)(a − b) to find 59² − 28².
36. 36.Use a² − b² = (a + b)(a − b) to find 81² − 59².
37. 37.Use (a − b)² = a² − 2ab + b² to find 84².
38. 38.Use a² − b² = (a + b)(a − b) to find 88² − 13².
39. 39.If a − b = 7 and ab = 8, what is a² + b²?
40. 40.Use a² − b² = (a + b)(a − b) to find 41² − 1².

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