Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 651 · 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 = 77, what is a² + b²?
2. 2.Use (a + b)² = a² + 2ab + b² to find 47².
3. 3.Use (a + b)(a − b) = a² − b² to find 108 × 92.
4. 4.If a − b = 1 and ab = 6, what is a² + b²?
5. 5.Use (a + b)(a − b) = a² − b² to find 41 × 39.
6. 6.Find the value of x² − 2xy + y² when x = 13 and y = 10.
7. 7.Use a² − b² = (a + b)(a − b) to find 94² − 7².
8. 8.Find the value of x² − 2xy + y² when x = 7 and y = 5.
9. 9.If a − b = 5 and ab = 66, what is a² + b²?
10. 10.Use a² − b² = (a + b)(a − b) to find 44² − 43².
11. 11.If a − b = 3 and ab = 40, what is a² + b²?
12. 12.Use (a + b)(a − b) = a² − b² to find 36 × 24.
13. 13.Use a² − b² = (a + b)(a − b) to find 51² − 8².
14. 14.Use (a + b)² = a² + 2ab + b² to find 35².
15. 15.Use a² − b² = (a + b)(a − b) to find 96² − 88².
16. 16.Find the value of x² + 2xy + y² when x = 6 and y = 5.
17. 17.Use (a − b)² = a² − 2ab + b² to find 84².
18. 18.If a − b = 4 and ab = 5, what is a² + b²?
19. 19.Find the value of x² + 2xy + y² when x = 9 and y = 1.
20. 20.Find the value of x² − 2xy + y² when x = 4 and y = 1.
21. 21.Find the value of x² − y² when x = 4 and y = 2.
22. 22.Use (a − b)² = a² − 2ab + b² to find 28².
23. 23.Find the value of x² − 2xy + y² when x = 5 and y = 4.
24. 24.Use (a − b)² = a² − 2ab + b² to find 13².
25. 25.If a + b = 12 and ab = 27, what is a² + b²?
26. 26.If a − b = 7 and ab = 60, what is a² + b²?
27. 27.Use (a − b)² = a² − 2ab + b² to find 44².
28. 28.Use (a − b)² = a² − 2ab + b² to find 18².
29. 29.Use (a + b)(a − b) = a² − b² to find 38 × 22.
30. 30.Use (a + b)² = a² + 2ab + b² to find 54².
31. 31.Use (a − b)² = a² − 2ab + b² to find 26².
32. 32.If a + b = 9 and ab = 20, what is a² + b²?
33. 33.Use (a + b)(a − b) = a² − b² to find 27 × 13.
34. 34.Find the value of x² + 2xy + y² when x = 15 and y = 5.
35. 35.Find the value of x² + 2xy + y² when x = 7 and y = 4.
36. 36.If a + b = 7 and ab = 6, what is a² + b²?
37. 37.Use (a + b)² = a² + 2ab + b² to find 17².
38. 38.Use a² − b² = (a + b)(a − b) to find 84² − 10².
39. 39.Use (a + b)² = a² + 2ab + b² to find 69².
40. 40.Use (a − b)² = a² − 2ab + b² to find 52².

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