Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 875 · 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 62² − 33².
2. 2.Use (a + b)(a − b) = a² − b² to find 55 × 45.
3. 3.If a + b = 8 and ab = 7, what is a² + b²?
4. 4.Use (a + b)² = a² + 2ab + b² to find 44².
5. 5.If a + b = 11 and ab = 30, what is a² + b²?
6. 6.If a − b = 3 and ab = 18, what is a² + b²?
7. 7.Use a² − b² = (a + b)(a − b) to find 82² − 24².
8. 8.Use a² − b² = (a + b)(a − b) to find 92² − 8².
9. 9.Find the value of x² − 2xy + y² when x = 15 and y = 3.
10. 10.Use (a + b)(a − b) = a² − b² to find 84 × 76.
11. 11.Use (a − b)² = a² − 2ab + b² to find 47².
12. 12.Use (a + b)(a − b) = a² − b² to find 71 × 69.
13. 13.Use (a + b)(a − b) = a² − b² to find 99 × 81.
14. 14.Use (a − b)² = a² − 2ab + b² to find 75².
15. 15.If a − b = 4 and ab = 21, what is a² + b²?
16. 16.Use (a + b)² = a² + 2ab + b² to find 48².
17. 17.If a − b = 10 and ab = 11, what is a² + b²?
18. 18.If a − b = 5 and ab = 36, what is a² + b²?
19. 19.Find the value of x² + 2xy + y² when x = 10 and y = 9.
20. 20.Use (a + b)² = a² + 2ab + b² to find 55².
21. 21.If a − b = 6 and ab = 55, what is a² + b²?
22. 22.Use (a − b)² = a² − 2ab + b² to find 48².
23. 23.Use (a + b)(a − b) = a² − b² to find 31 × 29.
24. 24.Find the value of x² − 2xy + y² when x = 9 and y = 3.
25. 25.Use a² − b² = (a + b)(a − b) to find 40² − 34².
26. 26.Use a² − b² = (a + b)(a − b) to find 61² − 27².
27. 27.Use a² − b² = (a + b)(a − b) to find 82² − 3².
28. 28.If a − b = 3 and ab = 88, what is a² + b²?
29. 29.Find the value of x² + 2xy + y² when x = 14 and y = 7.
30. 30.Use (a + b)(a − b) = a² − b² to find 105 × 95.
31. 31.Find the value of x² − 2xy + y² when x = 11 and y = 10.
32. 32.Use (a − b)² = a² − 2ab + b² to find 49².
33. 33.Use (a + b)² = a² + 2ab + b² to find 21².
34. 34.Find the value of x² − y² when x = 14 and y = 9.
35. 35.Find the value of x² − y² when x = 4 and y = 2.
36. 36.Use (a + b)(a − b) = a² − b² to find 33 × 27.
37. 37.Use (a − b)² = a² − 2ab + b² to find 32².
38. 38.Use a² − b² = (a + b)(a − b) to find 99² − 2².
39. 39.Use (a − b)² = a² − 2ab + b² to find 79².
40. 40.If a + b = 16 and ab = 60, what is a² + b²?

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