Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 261 · 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 52².
2. 2.Use (a + b)(a − b) = a² − b² to find 44 × 36.
3. 3.If a + b = 5 and ab = 6, what is a² + b²?
4. 4.Use (a − b)² = a² − 2ab + b² to find 18².
5. 5.If a − b = 2 and ab = 15, what is a² + b²?
6. 6.Use (a − b)² = a² − 2ab + b² to find 22².
7. 7.Use (a − b)² = a² − 2ab + b² to find 47².
8. 8.Use (a + b)(a − b) = a² − b² to find 39 × 21.
9. 9.Find the value of x² − 2xy + y² when x = 3 and y = 1.
10. 10.Use (a + b)² = a² + 2ab + b² to find 31².
11. 11.Use (a + b)² = a² + 2ab + b² to find 51².
12. 12.If a − b = 9 and ab = 36, what is a² + b²?
13. 13.Use a² − b² = (a + b)(a − b) to find 85² − 25².
14. 14.Find the value of x² − y² when x = 10 and y = 6.
15. 15.Find the value of x² − y² when x = 5 and y = 1.
16. 16.Use (a + b)² = a² + 2ab + b² to find 98².
17. 17.Use (a − b)² = a² − 2ab + b² to find 59².
18. 18.Use a² − b² = (a + b)(a − b) to find 79² − 53².
19. 19.Find the value of x² + 2xy + y² when x = 8 and y = 5.
20. 20.If a − b = 2 and ab = 35, what is a² + b²?
21. 21.Use a² − b² = (a + b)(a − b) to find 68² − 1².
22. 22.Use (a + b)(a − b) = a² − b² to find 85 × 75.
23. 23.Use (a + b)² = a² + 2ab + b² to find 67².
24. 24.Use a² − b² = (a + b)(a − b) to find 81² − 17².
25. 25.Use (a − b)² = a² − 2ab + b² to find 74².
26. 26.Use (a + b)(a − b) = a² − b² to find 106 × 94.
27. 27.If a − b = 1 and ab = 2, what is a² + b²?
28. 28.Use (a + b)(a − b) = a² − b² to find 97 × 83.
29. 29.If a + b = 6 and ab = 5, what is a² + b²?
30. 30.If a + b = 3 and ab = 2, what is a² + b²?
31. 31.Use a² − b² = (a + b)(a − b) to find 85² − 78².
32. 32.Find the value of x² − y² when x = 13 and y = 3.
33. 33.If a − b = 4 and ab = 5, what is a² + b²?
34. 34.Use (a + b)(a − b) = a² − b² to find 82 × 78.
35. 35.Use (a + b)² = a² + 2ab + b² to find 78².
36. 36.Find the value of x² − 2xy + y² when x = 12 and y = 1.
37. 37.If a + b = 7 and ab = 6, what is a² + b²?
38. 38.Use (a + b)(a − b) = a² − b² to find 98 × 82.
39. 39.Use (a + b)(a − b) = a² − b² to find 25 × 15.
40. 40.If a − b = 6 and ab = 72, what is a² + b²?

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