Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 142 · 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 38².
2. 2.If a − b = 1 and ab = 2, what is a² + b²?
3. 3.Use (a + b)(a − b) = a² − b² to find 71 × 69.
4. 4.Use (a − b)² = a² − 2ab + b² to find 79².
5. 5.Use (a + b)² = a² + 2ab + b² to find 87².
6. 6.Use (a + b)(a − b) = a² − b² to find 37 × 23.
7. 7.Find the value of x² − y² when x = 12 and y = 11.
8. 8.If a + b = 21 and ab = 110, what is a² + b²?
9. 9.If a − b = 1 and ab = 6, what is a² + b²?
10. 10.Find the value of x² + 2xy + y² when x = 15 and y = 8.
11. 11.Use (a − b)² = a² − 2ab + b² to find 17².
12. 12.Use (a + b)² = a² + 2ab + b² to find 51².
13. 13.Use (a + b)² = a² + 2ab + b² to find 49².
14. 14.If a + b = 7 and ab = 6, what is a² + b²?
15. 15.Use (a − b)² = a² − 2ab + b² to find 33².
16. 16.If a + b = 21 and ab = 108, what is a² + b²?
17. 17.Find the value of x² − 2xy + y² when x = 10 and y = 2.
18. 18.Find the value of x² + 2xy + y² when x = 5 and y = 1.
19. 19.Use a² − b² = (a + b)(a − b) to find 77² − 74².
20. 20.If a + b = 16 and ab = 55, what is a² + b²?
21. 21.Use (a − b)² = a² − 2ab + b² to find 78².
22. 22.Use (a + b)² = a² + 2ab + b² to find 11².
23. 23.Use a² − b² = (a + b)(a − b) to find 57² − 26².
24. 24.If a + b = 3 and ab = 2, what is a² + b²?
25. 25.Use (a + b)² = a² + 2ab + b² to find 16².
26. 26.Use (a + b)² = a² + 2ab + b² to find 73².
27. 27.Use (a + b)(a − b) = a² − b² to find 53 × 47.
28. 28.Use (a + b)(a − b) = a² − b² to find 22 × 18.
29. 29.Use a² − b² = (a + b)(a − b) to find 99² − 29².
30. 30.Use (a − b)² = a² − 2ab + b² to find 87².
31. 31.Find the value of x² − 2xy + y² when x = 4 and y = 1.
32. 32.Find the value of x² − 2xy + y² when x = 13 and y = 3.
33. 33.Use (a − b)² = a² − 2ab + b² to find 34².
34. 34.Use (a + b)(a − b) = a² − b² to find 28 × 12.
35. 35.If a − b = 2 and ab = 48, what is a² + b²?
36. 36.Use (a + b)² = a² + 2ab + b² to find 59².
37. 37.If a + b = 13 and ab = 22, what is a² + b²?
38. 38.Use (a + b)² = a² + 2ab + b² to find 23².
39. 39.If a − b = 1 and ab = 20, what is a² + b²?
40. 40.Use (a + b)² = a² + 2ab + b² to find 44².

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