Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 770 · 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 33².
2. 2.If a + b = 23 and ab = 132, what is a² + b²?
3. 3.Use (a + b)² = a² + 2ab + b² to find 107².
4. 4.Use a² − b² = (a + b)(a − b) to find 74² − 11².
5. 5.Use (a − b)² = a² − 2ab + b² to find 42².
6. 6.Use (a + b)(a − b) = a² − b² to find 88 × 72.
7. 7.Use (a + b)(a − b) = a² − b² to find 71 × 69.
8. 8.Find the value of x² + 2xy + y² when x = 6 and y = 4.
9. 9.Use (a + b)(a − b) = a² − b² to find 51 × 49.
10. 10.Use a² − b² = (a + b)(a − b) to find 26² − 21².
11. 11.Use (a + b)² = a² + 2ab + b² to find 53².
12. 12.If a + b = 10 and ab = 21, what is a² + b²?
13. 13.Use (a + b)² = a² + 2ab + b² to find 27².
14. 14.Use (a − b)² = a² − 2ab + b² to find 37².
15. 15.Use (a − b)² = a² − 2ab + b² to find 55².
16. 16.Find the value of x² + 2xy + y² when x = 7 and y = 5.
17. 17.Use (a − b)² = a² − 2ab + b² to find 21².
18. 18.Use (a − b)² = a² − 2ab + b² to find 58².
19. 19.Use (a + b)² = a² + 2ab + b² to find 57².
20. 20.Use (a + b)² = a² + 2ab + b² to find 26².
21. 21.Use (a + b)² = a² + 2ab + b² to find 38².
22. 22.If a + b = 10 and ab = 24, what is a² + b²?
23. 23.Use (a − b)² = a² − 2ab + b² to find 74².
24. 24.Use (a + b)(a − b) = a² − b² to find 96 × 84.
25. 25.If a − b = 2 and ab = 15, what is a² + b²?
26. 26.Use (a + b)² = a² + 2ab + b² to find 44².
27. 27.Find the value of x² + 2xy + y² when x = 7 and y = 6.
28. 28.Use (a + b)(a − b) = a² − b² to find 43 × 37.
29. 29.Use (a + b)(a − b) = a² − b² to find 97 × 83.
30. 30.Use (a − b)² = a² − 2ab + b² to find 86².
31. 31.Use (a + b)(a − b) = a² − b² to find 24 × 16.
32. 32.Use (a − b)² = a² − 2ab + b² to find 22².
33. 33.Use (a + b)² = a² + 2ab + b² to find 15².
34. 34.If a + b = 8 and ab = 15, what is a² + b²?
35. 35.Use (a + b)(a − b) = a² − b² to find 67 × 53.
36. 36.Use a² − b² = (a + b)(a − b) to find 83² − 58².
37. 37.Find the value of x² − y² when x = 12 and y = 5.
38. 38.Use (a + b)(a − b) = a² − b² to find 44 × 36.
39. 39.If a − b = 4 and ab = 12, what is a² + b²?
40. 40.Use (a − b)² = a² − 2ab + b² to find 38².

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