Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 883 · 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 a² − b² = (a + b)(a − b) to find 39² − 4².
2. 2.If a − b = 4 and ab = 5, what is a² + b²?
3. 3.Use (a + b)² = a² + 2ab + b² to find 39².
4. 4.Find the value of x² − 2xy + y² when x = 14 and y = 10.
5. 5.Use (a + b)² = a² + 2ab + b² to find 63².
6. 6.Use (a − b)² = a² − 2ab + b² to find 98².
7. 7.Use (a + b)(a − b) = a² − b² to find 61 × 59.
8. 8.Find the value of x² − y² when x = 3 and y = 1.
9. 9.Use (a − b)² = a² − 2ab + b² to find 49².
10. 10.Use (a + b)² = a² + 2ab + b² to find 74².
11. 11.Find the value of x² + 2xy + y² when x = 10 and y = 3.
12. 12.Find the value of x² + 2xy + y² when x = 8 and y = 1.
13. 13.If a + b = 7 and ab = 10, what is a² + b²?
14. 14.If a + b = 6 and ab = 5, what is a² + b²?
15. 15.Use (a + b)(a − b) = a² − b² to find 89 × 71.
16. 16.Use (a + b)(a − b) = a² − b² to find 57 × 43.
17. 17.Use (a + b)² = a² + 2ab + b² to find 81².
18. 18.Use a² − b² = (a + b)(a − b) to find 59² − 31².
19. 19.If a − b = 2 and ab = 48, what is a² + b²?
20. 20.Use (a − b)² = a² − 2ab + b² to find 59².
21. 21.If a + b = 11 and ab = 18, what is a² + b²?
22. 22.Use (a + b)² = a² + 2ab + b² to find 22².
23. 23.Use a² − b² = (a + b)(a − b) to find 89² − 54².
24. 24.If a − b = 4 and ab = 32, what is a² + b²?
25. 25.Use (a + b)² = a² + 2ab + b² to find 31².
26. 26.Use a² − b² = (a + b)(a − b) to find 52² − 29².
27. 27.Use (a − b)² = a² − 2ab + b² to find 79².
28. 28.Use (a − b)² = a² − 2ab + b² to find 29².
29. 29.Find the value of x² − y² when x = 8 and y = 4.
30. 30.Use (a + b)(a − b) = a² − b² to find 106 × 94.
31. 31.Use (a + b)(a − b) = a² − b² to find 54 × 46.
32. 32.If a − b = 5 and ab = 36, what is a² + b²?
33. 33.Use (a + b)² = a² + 2ab + b² to find 29².
34. 34.Find the value of x² − y² when x = 10 and y = 8.
35. 35.If a + b = 10 and ab = 21, what is a² + b²?
36. 36.Find the value of x² − 2xy + y² when x = 11 and y = 7.
37. 37.Find the value of x² + 2xy + y² when x = 9 and y = 6.
38. 38.Use (a + b)(a − b) = a² − b² to find 101 × 99.
39. 39.Use (a − b)² = a² − 2ab + b² to find 89².
40. 40.If a + b = 3 and ab = 2, what is a² + b²?

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