Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 719 · 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 69² − 24².
2. 2.If a − b = 2 and ab = 35, what is a² + b²?
3. 3.Use (a − b)² = a² − 2ab + b² to find 24².
4. 4.Use (a + b)(a − b) = a² − b² to find 56 × 44.
5. 5.Find the value of x² − y² when x = 3 and y = 1.
6. 6.Find the value of x² − 2xy + y² when x = 13 and y = 2.
7. 7.Use (a + b)(a − b) = a² − b² to find 58 × 42.
8. 8.Find the value of x² + 2xy + y² when x = 5 and y = 2.
9. 9.Use (a − b)² = a² − 2ab + b² to find 94².
10. 10.Use (a + b)² = a² + 2ab + b² to find 17².
11. 11.Find the value of x² − y² when x = 14 and y = 5.
12. 12.Find the value of x² + 2xy + y² when x = 14 and y = 13.
13. 13.Find the value of x² + 2xy + y² when x = 5 and y = 4.
14. 14.Use (a + b)(a − b) = a² − b² to find 43 × 37.
15. 15.Find the value of x² + 2xy + y² when x = 12 and y = 11.
16. 16.Use a² − b² = (a + b)(a − b) to find 35² − 1².
17. 17.Use (a + b)² = a² + 2ab + b² to find 79².
18. 18.Find the value of x² + 2xy + y² when x = 14 and y = 11.
19. 19.Find the value of x² − y² when x = 9 and y = 4.
20. 20.If a − b = 7 and ab = 8, what is a² + b²?
21. 21.Find the value of x² + 2xy + y² when x = 3 and y = 1.
22. 22.Use (a − b)² = a² − 2ab + b² to find 79².
23. 23.If a + b = 7 and ab = 6, what is a² + b²?
24. 24.Use a² − b² = (a + b)(a − b) to find 53² − 11².
25. 25.If a − b = 7 and ab = 18, what is a² + b²?
26. 26.Use a² − b² = (a + b)(a − b) to find 37² − 15².
27. 27.Use (a − b)² = a² − 2ab + b² to find 33².
28. 28.Find the value of x² − 2xy + y² when x = 6 and y = 1.
29. 29.Use a² − b² = (a + b)(a − b) to find 56² − 16².
30. 30.Use (a + b)² = a² + 2ab + b² to find 85².
31. 31.Use a² − b² = (a + b)(a − b) to find 99² − 50².
32. 32.Use (a − b)² = a² − 2ab + b² to find 23².
33. 33.Use (a + b)² = a² + 2ab + b² to find 97².
34. 34.If a + b = 9 and ab = 20, what is a² + b²?
35. 35.Use a² − b² = (a + b)(a − b) to find 67² − 23².
36. 36.Use (a + b)(a − b) = a² − b² to find 76 × 64.
37. 37.Use (a + b)(a − b) = a² − b² to find 38 × 22.
38. 38.Use (a + b)² = a² + 2ab + b² to find 102².
39. 39.Use (a + b)(a − b) = a² − b² to find 73 × 67.
40. 40.Find the value of x² + 2xy + y² when x = 4 and y = 3.

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