Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 668 · 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 42².
2. 2.Find the value of x² + 2xy + y² when x = 4 and y = 3.
3. 3.Use (a + b)(a − b) = a² − b² to find 25 × 15.
4. 4.If a + b = 9 and ab = 8, what is a² + b²?
5. 5.If a − b = 5 and ab = 24, what is a² + b²?
6. 6.Use (a − b)² = a² − 2ab + b² to find 78².
7. 7.Use (a + b)² = a² + 2ab + b² to find 62².
8. 8.If a + b = 7 and ab = 6, what is a² + b²?
9. 9.Use (a + b)² = a² + 2ab + b² to find 66².
10. 10.Use a² − b² = (a + b)(a − b) to find 48² − 43².
11. 11.Use (a − b)² = a² − 2ab + b² to find 41².
12. 12.Use (a + b)(a − b) = a² − b² to find 99 × 81.
13. 13.Find the value of x² − y² when x = 9 and y = 8.
14. 14.Use (a + b)² = a² + 2ab + b² to find 36².
15. 15.Find the value of x² − 2xy + y² when x = 11 and y = 2.
16. 16.Use (a + b)² = a² + 2ab + b² to find 12².
17. 17.Use (a − b)² = a² − 2ab + b² to find 96².
18. 18.Use (a + b)² = a² + 2ab + b² to find 39².
19. 19.If a + b = 3 and ab = 2, what is a² + b²?
20. 20.Use (a + b)(a − b) = a² − b² to find 55 × 45.
21. 21.If a + b = 14 and ab = 33, what is a² + b²?
22. 22.Use (a + b)² = a² + 2ab + b² to find 96².
23. 23.Use (a + b)² = a² + 2ab + b² to find 58².
24. 24.If a − b = 4 and ab = 60, what is a² + b²?
25. 25.Use (a + b)² = a² + 2ab + b² to find 108².
26. 26.Use a² − b² = (a + b)(a − b) to find 41² − 9².
27. 27.Use (a + b)² = a² + 2ab + b² to find 25².
28. 28.Find the value of x² + 2xy + y² when x = 9 and y = 4.
29. 29.Use a² − b² = (a + b)(a − b) to find 21² − 15².
30. 30.Use (a + b)(a − b) = a² − b² to find 64 × 56.
31. 31.Use (a − b)² = a² − 2ab + b² to find 32².
32. 32.Use (a + b)² = a² + 2ab + b² to find 87².
33. 33.If a − b = 1 and ab = 20, what is a² + b²?
34. 34.Use (a + b)² = a² + 2ab + b² to find 93².
35. 35.If a − b = 1 and ab = 110, what is a² + b²?
36. 36.Use a² − b² = (a + b)(a − b) to find 38² − 25².
37. 37.Use (a + b)² = a² + 2ab + b² to find 23².
38. 38.Use (a + b)(a − b) = a² − b² to find 28 × 12.
39. 39.Find the value of x² + 2xy + y² when x = 5 and y = 2.
40. 40.Use a² − b² = (a + b)(a − b) to find 29² − 20².

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