Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 172 · 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.If a + b = 19 and ab = 88, what is a² + b²?
2. 2.Use (a + b)² = a² + 2ab + b² to find 82².
3. 3.Find the value of x² − 2xy + y² when x = 5 and y = 2.
4. 4.Use a² − b² = (a + b)(a − b) to find 76² − 26².
5. 5.Use (a − b)² = a² − 2ab + b² to find 35².
6. 6.Find the value of x² − 2xy + y² when x = 9 and y = 1.
7. 7.Find the value of x² − y² when x = 13 and y = 12.
8. 8.If a − b = 1 and ab = 2, what is a² + b²?
9. 9.Use (a + b)² = a² + 2ab + b² to find 16².
10. 10.Use (a − b)² = a² − 2ab + b² to find 21².
11. 11.Use (a + b)² = a² + 2ab + b² to find 64².
12. 12.Use (a + b)(a − b) = a² − b² to find 21 × 19.
13. 13.Use (a + b)² = a² + 2ab + b² to find 99².
14. 14.Use (a + b)² = a² + 2ab + b² to find 32².
15. 15.Use (a + b)(a − b) = a² − b² to find 55 × 45.
16. 16.Use (a − b)² = a² − 2ab + b² to find 49².
17. 17.Use (a + b)² = a² + 2ab + b² to find 44².
18. 18.Use a² − b² = (a + b)(a − b) to find 75² − 34².
19. 19.Use a² − b² = (a + b)(a − b) to find 66² − 34².
20. 20.Use (a − b)² = a² − 2ab + b² to find 26².
21. 21.Use (a + b)(a − b) = a² − b² to find 23 × 17.
22. 22.Find the value of x² − y² when x = 5 and y = 1.
23. 23.Use (a + b)(a − b) = a² − b² to find 26 × 14.
24. 24.Use a² − b² = (a + b)(a − b) to find 40² − 12².
25. 25.If a − b = 6 and ab = 16, what is a² + b²?
26. 26.If a − b = 2 and ab = 3, what is a² + b²?
27. 27.Use (a + b)² = a² + 2ab + b² to find 22².
28. 28.Find the value of x² + 2xy + y² when x = 9 and y = 2.
29. 29.Find the value of x² − y² when x = 12 and y = 4.
30. 30.Use (a + b)² = a² + 2ab + b² to find 109².
31. 31.If a + b = 17 and ab = 60, what is a² + b²?
32. 32.Find the value of x² − 2xy + y² when x = 13 and y = 1.
33. 33.Use (a + b)² = a² + 2ab + b² to find 21².
34. 34.Use (a + b)² = a² + 2ab + b² to find 58².
35. 35.Use (a + b)² = a² + 2ab + b² to find 31².
36. 36.Use (a + b)² = a² + 2ab + b² to find 39².
37. 37.Use (a + b)² = a² + 2ab + b² to find 76².
38. 38.Use a² − b² = (a + b)(a − b) to find 51² − 35².
39. 39.Use (a − b)² = a² − 2ab + b² to find 57².
40. 40.Use (a + b)(a − b) = a² − b² to find 42 × 38.

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