Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 730 · 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 78 × 62.
2. 2.Use a² − b² = (a + b)(a − b) to find 71² − 4².
3. 3.Use (a − b)² = a² − 2ab + b² to find 28².
4. 4.If a − b = 3 and ab = 4, what is a² + b²?
5. 5.Use (a + b)² = a² + 2ab + b² to find 18².
6. 6.If a + b = 6 and ab = 5, what is a² + b²?
7. 7.If a − b = 5 and ab = 14, what is a² + b²?
8. 8.Use (a − b)² = a² − 2ab + b² to find 27².
9. 9.Use (a + b)² = a² + 2ab + b² to find 93².
10. 10.Use a² − b² = (a + b)(a − b) to find 63² − 11².
11. 11.Use (a + b)² = a² + 2ab + b² to find 71².
12. 12.Use (a + b)² = a² + 2ab + b² to find 43².
13. 13.Use (a − b)² = a² − 2ab + b² to find 56².
14. 14.Use (a − b)² = a² − 2ab + b² to find 44².
15. 15.Use (a − b)² = a² − 2ab + b² to find 85².
16. 16.If a + b = 14 and ab = 33, what is a² + b²?
17. 17.Use (a − b)² = a² − 2ab + b² to find 58².
18. 18.Find the value of x² + 2xy + y² when x = 3 and y = 2.
19. 19.If a − b = 3 and ab = 10, what is a² + b²?
20. 20.Use a² − b² = (a + b)(a − b) to find 87² − 52².
21. 21.Use a² − b² = (a + b)(a − b) to find 75² − 33².
22. 22.If a + b = 5 and ab = 4, what is a² + b²?
23. 23.Use (a − b)² = a² − 2ab + b² to find 89².
24. 24.If a + b = 3 and ab = 2, what is a² + b²?
25. 25.Use (a + b)² = a² + 2ab + b² to find 87².
26. 26.Use (a + b)² = a² + 2ab + b² to find 11².
27. 27.Use (a + b)(a − b) = a² − b² to find 104 × 96.
28. 28.If a + b = 19 and ab = 88, what is a² + b²?
29. 29.Use (a − b)² = a² − 2ab + b² to find 48².
30. 30.Use a² − b² = (a + b)(a − b) to find 52² − 35².
31. 31.Use (a + b)(a − b) = a² − b² to find 22 × 18.
32. 32.Use (a + b)(a − b) = a² − b² to find 45 × 35.
33. 33.Use (a + b)² = a² + 2ab + b² to find 81².
34. 34.Use (a + b)² = a² + 2ab + b² to find 62².
35. 35.If a + b = 15 and ab = 44, what is a² + b²?
36. 36.Use a² − b² = (a + b)(a − b) to find 85² − 54².
37. 37.Use a² − b² = (a + b)(a − b) to find 42² − 27².
38. 38.Find the value of x² + 2xy + y² when x = 4 and y = 1.
39. 39.If a + b = 4 and ab = 3, what is a² + b²?
40. 40.Use (a − b)² = a² − 2ab + b² to find 99².

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