Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 711 · 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 24² − 18².
2. 2.If a − b = 1 and ab = 30, what is a² + b²?
3. 3.Use a² − b² = (a + b)(a − b) to find 39² − 2².
4. 4.If a + b = 10 and ab = 16, what is a² + b²?
5. 5.Use (a − b)² = a² − 2ab + b² to find 65².
6. 6.Use (a + b)² = a² + 2ab + b² to find 58².
7. 7.If a − b = 1 and ab = 2, what is a² + b²?
8. 8.Use (a + b)(a − b) = a² − b² to find 108 × 92.
9. 9.Use (a + b)² = a² + 2ab + b² to find 29².
10. 10.Use (a + b)(a − b) = a² − b² to find 72 × 68.
11. 11.Use (a − b)² = a² − 2ab + b² to find 28².
12. 12.Use a² − b² = (a + b)(a − b) to find 81² − 70².
13. 13.If a − b = 6 and ab = 7, what is a² + b²?
14. 14.Use (a + b)(a − b) = a² − b² to find 91 × 89.
15. 15.Use (a + b)(a − b) = a² − b² to find 88 × 72.
16. 16.Use (a + b)² = a² + 2ab + b² to find 67².
17. 17.If a + b = 10 and ab = 9, what is a² + b²?
18. 18.Use (a − b)² = a² − 2ab + b² to find 17².
19. 19.Use a² − b² = (a + b)(a − b) to find 87² − 52².
20. 20.Find the value of x² − 2xy + y² when x = 9 and y = 4.
21. 21.If a − b = 2 and ab = 3, what is a² + b²?
22. 22.Use (a + b)² = a² + 2ab + b² to find 83².
23. 23.If a + b = 8 and ab = 12, what is a² + b²?
24. 24.Use a² − b² = (a + b)(a − b) to find 55² − 15².
25. 25.Find the value of x² + 2xy + y² when x = 8 and y = 1.
26. 26.Use (a + b)² = a² + 2ab + b² to find 15².
27. 27.Use a² − b² = (a + b)(a − b) to find 49² − 32².
28. 28.Find the value of x² + 2xy + y² when x = 9 and y = 6.
29. 29.Use (a − b)² = a² − 2ab + b² to find 93².
30. 30.Use (a + b)(a − b) = a² − b² to find 77 × 63.
31. 31.Find the value of x² + 2xy + y² when x = 9 and y = 5.
32. 32.Find the value of x² − 2xy + y² when x = 7 and y = 3.
33. 33.Use (a − b)² = a² − 2ab + b² to find 16².
34. 34.If a − b = 2 and ab = 120, what is a² + b²?
35. 35.Use (a + b)(a − b) = a² − b² to find 34 × 26.
36. 36.Find the value of x² + 2xy + y² when x = 7 and y = 6.
37. 37.Use a² − b² = (a + b)(a − b) to find 41² − 11².
38. 38.Use (a + b)(a − b) = a² − b² to find 99 × 81.
39. 39.Use (a + b)² = a² + 2ab + b² to find 76².
40. 40.If a + b = 21 and ab = 110, what is a² + b²?

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