Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 914 · 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 97² − 22².
2. 2.Use (a + b)(a − b) = a² − b² to find 25 × 15.
3. 3.Use (a − b)² = a² − 2ab + b² to find 68².
4. 4.Find the value of x² − 2xy + y² when x = 3 and y = 1.
5. 5.Use a² − b² = (a + b)(a − b) to find 28² − 14².
6. 6.Use a² − b² = (a + b)(a − b) to find 44² − 13².
7. 7.Use (a + b)² = a² + 2ab + b² to find 14².
8. 8.Use (a + b)² = a² + 2ab + b² to find 72².
9. 9.If a − b = 7 and ab = 18, what is a² + b²?
10. 10.Use (a − b)² = a² − 2ab + b² to find 57².
11. 11.Use (a − b)² = a² − 2ab + b² to find 29².
12. 12.Use (a + b)² = a² + 2ab + b² to find 44².
13. 13.Find the value of x² − y² when x = 13 and y = 1.
14. 14.Use (a + b)² = a² + 2ab + b² to find 22².
15. 15.Use (a − b)² = a² − 2ab + b² to find 92².
16. 16.If a + b = 18 and ab = 72, what is a² + b²?
17. 17.Find the value of x² − y² when x = 11 and y = 3.
18. 18.Use a² − b² = (a + b)(a − b) to find 44² − 35².
19. 19.Use (a + b)² = a² + 2ab + b² to find 16².
20. 20.Find the value of x² − y² when x = 7 and y = 3.
21. 21.Use (a + b)(a − b) = a² − b² to find 22 × 18.
22. 22.Use (a + b)(a − b) = a² − b² to find 71 × 69.
23. 23.Find the value of x² + 2xy + y² when x = 9 and y = 5.
24. 24.Use (a − b)² = a² − 2ab + b² to find 72².
25. 25.Use (a + b)(a − b) = a² − b² to find 92 × 88.
26. 26.Use a² − b² = (a + b)(a − b) to find 82² − 51².
27. 27.Use (a + b)(a − b) = a² − b² to find 33 × 27.
28. 28.Use (a − b)² = a² − 2ab + b² to find 89².
29. 29.Use (a + b)² = a² + 2ab + b² to find 101².
30. 30.Use (a − b)² = a² − 2ab + b² to find 22².
31. 31.If a − b = 1 and ab = 2, what is a² + b²?
32. 32.Use (a + b)² = a² + 2ab + b² to find 43².
33. 33.If a − b = 7 and ab = 8, what is a² + b²?
34. 34.Use (a + b)(a − b) = a² − b² to find 34 × 26.
35. 35.Find the value of x² − y² when x = 6 and y = 1.
36. 36.Use a² − b² = (a + b)(a − b) to find 81² − 5².
37. 37.Find the value of x² − y² when x = 4 and y = 3.
38. 38.Use (a + b)(a − b) = a² − b² to find 26 × 14.
39. 39.If a + b = 19 and ab = 88, what is a² + b²?
40. 40.Use (a + b)(a − b) = a² − b² to find 82 × 78.

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