Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 798 · 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)(a − b) = a² − b² to find 103 × 97.
2. 2.If a − b = 5 and ab = 66, what is a² + b²?
3. 3.Use (a − b)² = a² − 2ab + b² to find 46².
4. 4.Find the value of x² + 2xy + y² when x = 3 and y = 2.
5. 5.Find the value of x² − y² when x = 7 and y = 1.
6. 6.Find the value of x² + 2xy + y² when x = 13 and y = 12.
7. 7.Use (a − b)² = a² − 2ab + b² to find 59².
8. 8.Find the value of x² − y² when x = 7 and y = 5.
9. 9.Use (a + b)² = a² + 2ab + b² to find 47².
10. 10.Use a² − b² = (a + b)(a − b) to find 45² − 13².
11. 11.Use (a + b)² = a² + 2ab + b² to find 36².
12. 12.Use (a + b)² = a² + 2ab + b² to find 87².
13. 13.If a − b = 1 and ab = 2, what is a² + b²?
14. 14.Use (a + b)(a − b) = a² − b² to find 73 × 67.
15. 15.If a − b = 7 and ab = 44, what is a² + b²?
16. 16.Use (a − b)² = a² − 2ab + b² to find 37².
17. 17.Use a² − b² = (a + b)(a − b) to find 78² − 6².
18. 18.If a + b = 23 and ab = 132, what is a² + b²?
19. 19.Use (a − b)² = a² − 2ab + b² to find 76².
20. 20.Use (a + b)² = a² + 2ab + b² to find 103².
21. 21.Find the value of x² + 2xy + y² when x = 11 and y = 1.
22. 22.If a − b = 5 and ab = 6, what is a² + b²?
23. 23.Use (a − b)² = a² − 2ab + b² to find 65².
24. 24.Use a² − b² = (a + b)(a − b) to find 55² − 46².
25. 25.Use (a + b)(a − b) = a² − b² to find 95 × 85.
26. 26.If a + b = 6 and ab = 5, what is a² + b²?
27. 27.Use (a + b)² = a² + 2ab + b² to find 61².
28. 28.Find the value of x² − 2xy + y² when x = 10 and y = 9.
29. 29.Find the value of x² − y² when x = 4 and y = 3.
30. 30.Use a² − b² = (a + b)(a − b) to find 43² − 3².
31. 31.If a + b = 6 and ab = 8, what is a² + b²?
32. 32.Use a² − b² = (a + b)(a − b) to find 87² − 22².
33. 33.Use (a + b)(a − b) = a² − b² to find 67 × 53.
34. 34.Use (a − b)² = a² − 2ab + b² to find 66².
35. 35.Find the value of x² + 2xy + y² when x = 11 and y = 9.
36. 36.Find the value of x² − y² when x = 11 and y = 1.
37. 37.Find the value of x² − y² when x = 6 and y = 5.
38. 38.Use (a + b)² = a² + 2ab + b² to find 85².
39. 39.Use a² − b² = (a + b)(a − b) to find 71² − 14².
40. 40.Use (a + b)² = a² + 2ab + b² to find 66².

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