Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 588 · 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 56².
2. 2.Use (a − b)² = a² − 2ab + b² to find 14².
3. 3.Use (a + b)² = a² + 2ab + b² to find 21².
4. 4.Use (a + b)² = a² + 2ab + b² to find 55².
5. 5.Use (a + b)² = a² + 2ab + b² to find 49².
6. 6.Use (a + b)(a − b) = a² − b² to find 88 × 72.
7. 7.Use (a − b)² = a² − 2ab + b² to find 28².
8. 8.Use a² − b² = (a + b)(a − b) to find 37² − 13².
9. 9.Use (a + b)(a − b) = a² − b² to find 51 × 49.
10. 10.Use (a + b)² = a² + 2ab + b² to find 65².
11. 11.Find the value of x² + 2xy + y² when x = 8 and y = 3.
12. 12.Use (a + b)(a − b) = a² − b² to find 41 × 39.
13. 13.Use (a + b)(a − b) = a² − b² to find 39 × 21.
14. 14.Use (a − b)² = a² − 2ab + b² to find 78².
15. 15.Use (a + b)(a − b) = a² − b² to find 24 × 16.
16. 16.If a + b = 3 and ab = 2, what is a² + b²?
17. 17.Use (a + b)² = a² + 2ab + b² to find 56².
18. 18.Find the value of x² + 2xy + y² when x = 7 and y = 2.
19. 19.Use (a + b)² = a² + 2ab + b² to find 71².
20. 20.If a + b = 14 and ab = 33, what is a² + b²?
21. 21.Use (a + b)(a − b) = a² − b² to find 31 × 29.
22. 22.Use (a − b)² = a² − 2ab + b² to find 59².
23. 23.Use (a + b)(a − b) = a² − b² to find 21 × 19.
24. 24.Use (a + b)² = a² + 2ab + b² to find 109².
25. 25.Use (a + b)² = a² + 2ab + b² to find 26².
26. 26.Use (a − b)² = a² − 2ab + b² to find 39².
27. 27.Use (a + b)² = a² + 2ab + b² to find 77².
28. 28.Use (a − b)² = a² − 2ab + b² to find 64².
29. 29.Use a² − b² = (a + b)(a − b) to find 35² − 21².
30. 30.Use (a − b)² = a² − 2ab + b² to find 34².
31. 31.If a + b = 14 and ab = 45, what is a² + b²?
32. 32.Use (a − b)² = a² − 2ab + b² to find 87².
33. 33.Use (a + b)² = a² + 2ab + b² to find 107².
34. 34.If a − b = 1 and ab = 110, what is a² + b²?
35. 35.Use a² − b² = (a + b)(a − b) to find 71² − 36².
36. 36.Use a² − b² = (a + b)(a − b) to find 74² − 3².
37. 37.Use a² − b² = (a + b)(a − b) to find 22² − 8².
38. 38.Use (a − b)² = a² − 2ab + b² to find 23².
39. 39.Use (a + b)² = a² + 2ab + b² to find 92².
40. 40.If a − b = 2 and ab = 48, what is a² + b²?

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