Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 481 · 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.If a − b = 4 and ab = 5, what is a² + b²?
2. 2.Use (a + b)(a − b) = a² − b² to find 48 × 32.
3. 3.Use (a + b)² = a² + 2ab + b² to find 44².
4. 4.Use (a + b)(a − b) = a² − b² to find 59 × 41.
5. 5.Use a² − b² = (a + b)(a − b) to find 36² − 20².
6. 6.If a − b = 4 and ab = 45, what is a² + b²?
7. 7.Use (a − b)² = a² − 2ab + b² to find 98².
8. 8.Use (a + b)(a − b) = a² − b² to find 79 × 61.
9. 9.Find the value of x² − 2xy + y² when x = 3 and y = 1.
10. 10.Find the value of x² − 2xy + y² when x = 12 and y = 3.
11. 11.Use (a + b)² = a² + 2ab + b² to find 81².
12. 12.Find the value of x² − y² when x = 9 and y = 4.
13. 13.Use (a + b)² = a² + 2ab + b² to find 53².
14. 14.If a + b = 6 and ab = 8, what is a² + b²?
15. 15.Use a² − b² = (a + b)(a − b) to find 68² − 54².
16. 16.Use a² − b² = (a + b)(a − b) to find 55² − 49².
17. 17.If a − b = 2 and ab = 24, what is a² + b²?
18. 18.If a − b = 3 and ab = 4, what is a² + b²?
19. 19.Find the value of x² + 2xy + y² when x = 14 and y = 6.
20. 20.If a + b = 5 and ab = 6, what is a² + b²?
21. 21.Use (a + b)(a − b) = a² − b² to find 35 × 25.
22. 22.Use a² − b² = (a + b)(a − b) to find 63² − 43².
23. 23.Find the value of x² + 2xy + y² when x = 8 and y = 5.
24. 24.Use a² − b² = (a + b)(a − b) to find 39² − 26².
25. 25.Use (a − b)² = a² − 2ab + b² to find 57².
26. 26.Use (a − b)² = a² − 2ab + b² to find 91².
27. 27.Use (a − b)² = a² − 2ab + b² to find 64².
28. 28.Use (a + b)² = a² + 2ab + b² to find 86².
29. 29.Use a² − b² = (a + b)(a − b) to find 72² − 54².
30. 30.Use (a − b)² = a² − 2ab + b² to find 63².
31. 31.If a + b = 10 and ab = 21, what is a² + b²?
32. 32.Use a² − b² = (a + b)(a − b) to find 29² − 26².
33. 33.Use (a − b)² = a² − 2ab + b² to find 34².
34. 34.Use (a + b)² = a² + 2ab + b² to find 18².
35. 35.Use a² − b² = (a + b)(a − b) to find 36² − 29².
36. 36.Use (a − b)² = a² − 2ab + b² to find 88².
37. 37.If a + b = 13 and ab = 36, what is a² + b²?
38. 38.Use (a + b)² = a² + 2ab + b² to find 84².
39. 39.If a − b = 1 and ab = 2, what is a² + b²?
40. 40.Use (a + b)² = a² + 2ab + b² to find 95².

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