Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 772 · 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 = 19 and ab = 84, what is a² + b²?
2. 2.Use a² − b² = (a + b)(a − b) to find 20² − 14².
3. 3.Use (a + b)² = a² + 2ab + b² to find 62².
4. 4.If a − b = 1 and ab = 20, what is a² + b²?
5. 5.Find the value of x² − 2xy + y² when x = 14 and y = 9.
6. 6.Find the value of x² − 2xy + y² when x = 8 and y = 7.
7. 7.If a + b = 7 and ab = 12, what is a² + b²?
8. 8.Use (a + b)(a − b) = a² − b² to find 32 × 28.
9. 9.If a + b = 17 and ab = 66, what is a² + b²?
10. 10.Find the value of x² + 2xy + y² when x = 6 and y = 4.
11. 11.Use (a − b)² = a² − 2ab + b² to find 44².
12. 12.Find the value of x² − y² when x = 10 and y = 2.
13. 13.Find the value of x² − 2xy + y² when x = 5 and y = 2.
14. 14.Use (a + b)² = a² + 2ab + b² to find 53².
15. 15.Use (a − b)² = a² − 2ab + b² to find 17².
16. 16.Use (a − b)² = a² − 2ab + b² to find 81².
17. 17.Use (a − b)² = a² − 2ab + b² to find 99².
18. 18.Use a² − b² = (a + b)(a − b) to find 42² − 1².
19. 19.If a + b = 12 and ab = 20, what is a² + b²?
20. 20.Use a² − b² = (a + b)(a − b) to find 32² − 26².
21. 21.Use (a − b)² = a² − 2ab + b² to find 18².
22. 22.Use (a + b)² = a² + 2ab + b² to find 13².
23. 23.Use (a + b)² = a² + 2ab + b² to find 91².
24. 24.If a − b = 3 and ab = 70, what is a² + b²?
25. 25.Find the value of x² + 2xy + y² when x = 5 and y = 2.
26. 26.Find the value of x² + 2xy + y² when x = 10 and y = 4.
27. 27.Use a² − b² = (a + b)(a − b) to find 23² − 15².
28. 28.Use (a − b)² = a² − 2ab + b² to find 47².
29. 29.Use (a − b)² = a² − 2ab + b² to find 79².
30. 30.Use a² − b² = (a + b)(a − b) to find 21² − 19².
31. 31.If a + b = 15 and ab = 56, what is a² + b²?
32. 32.Use a² − b² = (a + b)(a − b) to find 31² − 6².
33. 33.Find the value of x² + 2xy + y² when x = 11 and y = 1.
34. 34.Use a² − b² = (a + b)(a − b) to find 39² − 15².
35. 35.Use (a + b)(a − b) = a² − b² to find 37 × 23.
36. 36.If a − b = 6 and ab = 40, what is a² + b²?
37. 37.Use a² − b² = (a + b)(a − b) to find 76² − 41².
38. 38.Use (a − b)² = a² − 2ab + b² to find 51².
39. 39.Use a² − b² = (a + b)(a − b) to find 98² − 12².
40. 40.If a − b = 1 and ab = 6, what is a² + b²?

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