Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 750 · 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 a² − b² = (a + b)(a − b) to find 23² − 1².
2. 2.If a − b = 3 and ab = 4, what is a² + b²?
3. 3.If a − b = 4 and ab = 60, what is a² + b²?
4. 4.Use (a − b)² = a² − 2ab + b² to find 23².
5. 5.Find the value of x² − 2xy + y² when x = 6 and y = 2.
6. 6.Use a² − b² = (a + b)(a − b) to find 74² − 56².
7. 7.Use (a + b)(a − b) = a² − b² to find 106 × 94.
8. 8.If a + b = 7 and ab = 10, what is a² + b²?
9. 9.Find the value of x² − y² when x = 12 and y = 2.
10. 10.Find the value of x² + 2xy + y² when x = 8 and y = 5.
11. 11.Use (a − b)² = a² − 2ab + b² to find 45².
12. 12.If a + b = 11 and ab = 30, what is a² + b²?
13. 13.Find the value of x² + 2xy + y² when x = 5 and y = 3.
14. 14.If a + b = 3 and ab = 2, what is a² + b²?
15. 15.If a − b = 5 and ab = 24, what is a² + b²?
16. 16.Use (a + b)(a − b) = a² − b² to find 84 × 76.
17. 17.Find the value of x² − 2xy + y² when x = 11 and y = 1.
18. 18.Use a² − b² = (a + b)(a − b) to find 55² − 3².
19. 19.Use (a + b)² = a² + 2ab + b² to find 46².
20. 20.If a + b = 8 and ab = 12, what is a² + b²?
21. 21.If a + b = 11 and ab = 18, what is a² + b²?
22. 22.Use (a + b)² = a² + 2ab + b² to find 41².
23. 23.Find the value of x² − y² when x = 13 and y = 10.
24. 24.Use a² − b² = (a + b)(a − b) to find 46² − 23².
25. 25.Find the value of x² − y² when x = 5 and y = 1.
26. 26.Use (a + b)² = a² + 2ab + b² to find 34².
27. 27.Find the value of x² + 2xy + y² when x = 9 and y = 7.
28. 28.Use (a + b)² = a² + 2ab + b² to find 81².
29. 29.If a + b = 13 and ab = 22, what is a² + b²?
30. 30.Find the value of x² + 2xy + y² when x = 7 and y = 6.
31. 31.Use (a + b)(a − b) = a² − b² to find 82 × 78.
32. 32.If a − b = 4 and ab = 45, what is a² + b²?
33. 33.Use a² − b² = (a + b)(a − b) to find 84² − 35².
34. 34.If a − b = 1 and ab = 6, what is a² + b²?
35. 35.Use a² − b² = (a + b)(a − b) to find 56² − 29².
36. 36.Use (a − b)² = a² − 2ab + b² to find 44².
37. 37.Use a² − b² = (a + b)(a − b) to find 67² − 23².
38. 38.Use (a + b)(a − b) = a² − b² to find 28 × 12.
39. 39.Use (a − b)² = a² − 2ab + b² to find 48².
40. 40.Use a² − b² = (a + b)(a − b) to find 69² − 23².

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