Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 565 · 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 43².
2. 2.Use (a + b)² = a² + 2ab + b² to find 49².
3. 3.Use (a − b)² = a² − 2ab + b² to find 26².
4. 4.If a − b = 1 and ab = 2, what is a² + b²?
5. 5.Use a² − b² = (a + b)(a − b) to find 72² − 33².
6. 6.Find the value of x² − y² when x = 12 and y = 2.
7. 7.Find the value of x² − 2xy + y² when x = 14 and y = 11.
8. 8.Use a² − b² = (a + b)(a − b) to find 25² − 2².
9. 9.Use a² − b² = (a + b)(a − b) to find 24² − 16².
10. 10.Use (a + b)(a − b) = a² − b² to find 73 × 67.
11. 11.Use (a + b)(a − b) = a² − b² to find 56 × 44.
12. 12.Use a² − b² = (a + b)(a − b) to find 27² − 13².
13. 13.Use (a + b)(a − b) = a² − b² to find 98 × 82.
14. 14.Use (a + b)(a − b) = a² − b² to find 25 × 15.
15. 15.If a + b = 5 and ab = 6, what is a² + b²?
16. 16.Use (a − b)² = a² − 2ab + b² to find 75².
17. 17.If a − b = 6 and ab = 40, what is a² + b²?
18. 18.Use a² − b² = (a + b)(a − b) to find 55² − 35².
19. 19.Find the value of x² − y² when x = 9 and y = 1.
20. 20.Use a² − b² = (a + b)(a − b) to find 25² − 10².
21. 21.Find the value of x² + 2xy + y² when x = 6 and y = 5.
22. 22.Use (a + b)(a − b) = a² − b² to find 103 × 97.
23. 23.Use (a + b)² = a² + 2ab + b² to find 41².
24. 24.Find the value of x² + 2xy + y² when x = 4 and y = 2.
25. 25.If a + b = 5 and ab = 4, what is a² + b²?
26. 26.Use (a + b)² = a² + 2ab + b² to find 14².
27. 27.Use a² − b² = (a + b)(a − b) to find 21² − 6².
28. 28.Use (a − b)² = a² − 2ab + b² to find 25².
29. 29.Use (a − b)² = a² − 2ab + b² to find 39².
30. 30.Use (a − b)² = a² − 2ab + b² to find 44².
31. 31.Use a² − b² = (a + b)(a − b) to find 81² − 21².
32. 32.Use (a + b)² = a² + 2ab + b² to find 97².
33. 33.Use (a + b)² = a² + 2ab + b² to find 56².
34. 34.Find the value of x² − y² when x = 3 and y = 1.
35. 35.Use a² − b² = (a + b)(a − b) to find 60² − 58².
36. 36.Use (a + b)(a − b) = a² − b² to find 22 × 18.
37. 37.Use (a + b)² = a² + 2ab + b² to find 42².
38. 38.Use a² − b² = (a + b)(a − b) to find 52² − 5².
39. 39.Find the value of x² − 2xy + y² when x = 5 and y = 4.
40. 40.If a − b = 4 and ab = 12, what is a² + b²?

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