Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 608 · 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.Find the value of x² − 2xy + y² when x = 5 and y = 3.
2. 2.Use a² − b² = (a + b)(a − b) to find 46² − 1².
3. 3.If a − b = 1 and ab = 42, what is a² + b²?
4. 4.Use (a − b)² = a² − 2ab + b² to find 13².
5. 5.Find the value of x² − y² when x = 8 and y = 7.
6. 6.If a + b = 5 and ab = 6, what is a² + b²?
7. 7.Use a² − b² = (a + b)(a − b) to find 71² − 6².
8. 8.Use (a − b)² = a² − 2ab + b² to find 89².
9. 9.Use (a + b)(a − b) = a² − b² to find 41 × 39.
10. 10.If a + b = 7 and ab = 10, what is a² + b²?
11. 11.Find the value of x² + 2xy + y² when x = 4 and y = 1.
12. 12.Use a² − b² = (a + b)(a − b) to find 88² − 59².
13. 13.Find the value of x² + 2xy + y² when x = 10 and y = 8.
14. 14.Find the value of x² − y² when x = 11 and y = 4.
15. 15.Use a² − b² = (a + b)(a − b) to find 44² − 6².
16. 16.Find the value of x² + 2xy + y² when x = 10 and y = 3.
17. 17.Use (a + b)(a − b) = a² − b² to find 72 × 68.
18. 18.Find the value of x² − y² when x = 3 and y = 1.
19. 19.If a + b = 16 and ab = 63, what is a² + b²?
20. 20.Use (a + b)² = a² + 2ab + b² to find 48².
21. 21.Use (a + b)² = a² + 2ab + b² to find 94².
22. 22.If a + b = 11 and ab = 10, what is a² + b²?
23. 23.Use a² − b² = (a + b)(a − b) to find 38² − 4².
24. 24.Find the value of x² − 2xy + y² when x = 4 and y = 1.
25. 25.Use (a − b)² = a² − 2ab + b² to find 92².
26. 26.Find the value of x² + 2xy + y² when x = 11 and y = 4.
27. 27.Use a² − b² = (a + b)(a − b) to find 29² − 12².
28. 28.Find the value of x² − y² when x = 10 and y = 1.
29. 29.If a + b = 19 and ab = 84, what is a² + b²?
30. 30.Use (a + b)² = a² + 2ab + b² to find 45².
31. 31.Find the value of x² − 2xy + y² when x = 7 and y = 1.
32. 32.Use (a + b)(a − b) = a² − b² to find 63 × 57.
33. 33.Find the value of x² + 2xy + y² when x = 6 and y = 1.
34. 34.If a + b = 15 and ab = 44, what is a² + b²?
35. 35.Find the value of x² + 2xy + y² when x = 8 and y = 2.
36. 36.Use (a − b)² = a² − 2ab + b² to find 28².
37. 37.Find the value of x² − 2xy + y² when x = 7 and y = 5.
38. 38.Use a² − b² = (a + b)(a − b) to find 32² − 19².
39. 39.Find the value of x² − 2xy + y² when x = 4 and y = 2.
40. 40.If a − b = 4 and ab = 45, what is a² + b²?

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