Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 704 · 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 106².
2. 2.Use a² − b² = (a + b)(a − b) to find 25² − 23².
3. 3.If a − b = 2 and ab = 3, what is a² + b²?
4. 4.Use (a + b)² = a² + 2ab + b² to find 24².
5. 5.Use (a + b)(a − b) = a² − b² to find 62 × 58.
6. 6.Use (a + b)² = a² + 2ab + b² to find 84².
7. 7.Find the value of x² − 2xy + y² when x = 7 and y = 4.
8. 8.Use (a − b)² = a² − 2ab + b² to find 28².
9. 9.Use (a − b)² = a² − 2ab + b² to find 42².
10. 10.Use (a + b)² = a² + 2ab + b² to find 91².
11. 11.Use (a + b)(a − b) = a² − b² to find 25 × 15.
12. 12.Use (a + b)(a − b) = a² − b² to find 21 × 19.
13. 13.Use (a + b)(a − b) = a² − b² to find 109 × 91.
14. 14.Use a² − b² = (a + b)(a − b) to find 71² − 19².
15. 15.Use (a + b)² = a² + 2ab + b² to find 18².
16. 16.If a + b = 6 and ab = 8, what is a² + b²?
17. 17.Use (a + b)(a − b) = a² − b² to find 79 × 61.
18. 18.Use (a + b)(a − b) = a² − b² to find 67 × 53.
19. 19.Use (a + b)(a − b) = a² − b² to find 28 × 12.
20. 20.If a − b = 5 and ab = 66, what is a² + b²?
21. 21.Use (a + b)(a − b) = a² − b² to find 72 × 68.
22. 22.Use (a + b)² = a² + 2ab + b² to find 76².
23. 23.Use (a + b)² = a² + 2ab + b² to find 45².
24. 24.Use a² − b² = (a + b)(a − b) to find 68² − 30².
25. 25.Find the value of x² + 2xy + y² when x = 8 and y = 1.
26. 26.If a + b = 9 and ab = 18, what is a² + b²?
27. 27.If a − b = 1 and ab = 72, what is a² + b²?
28. 28.Use (a + b)² = a² + 2ab + b² to find 99².
29. 29.Use a² − b² = (a + b)(a − b) to find 31² − 13².
30. 30.Use (a − b)² = a² − 2ab + b² to find 31².
31. 31.Find the value of x² − 2xy + y² when x = 11 and y = 8.
32. 32.Use (a + b)² = a² + 2ab + b² to find 104².
33. 33.Use a² − b² = (a + b)(a − b) to find 89² − 22².
34. 34.Use (a + b)² = a² + 2ab + b² to find 92².
35. 35.Find the value of x² + 2xy + y² when x = 13 and y = 10.
36. 36.Find the value of x² − y² when x = 14 and y = 12.
37. 37.If a + b = 14 and ab = 24, what is a² + b²?
38. 38.Use a² − b² = (a + b)(a − b) to find 70² − 18².
39. 39.Find the value of x² + 2xy + y² when x = 7 and y = 2.
40. 40.If a − b = 3 and ab = 54, what is a² + b²?

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