Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 760 · 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)² = a² − 2ab + b² to find 24².
2. 2.Use a² − b² = (a + b)(a − b) to find 49² − 6².
3. 3.Use a² − b² = (a + b)(a − b) to find 81² − 57².
4. 4.If a + b = 12 and ab = 20, what is a² + b²?
5. 5.Use (a + b)(a − b) = a² − b² to find 92 × 88.
6. 6.Use (a + b)(a − b) = a² − b² to find 62 × 58.
7. 7.Use (a + b)(a − b) = a² − b² to find 64 × 56.
8. 8.Find the value of x² + 2xy + y² when x = 5 and y = 4.
9. 9.Use a² − b² = (a + b)(a − b) to find 24² − 1².
10. 10.If a − b = 10 and ab = 24, what is a² + b²?
11. 11.Use a² − b² = (a + b)(a − b) to find 49² − 40².
12. 12.If a + b = 3 and ab = 2, what is a² + b²?
13. 13.Find the value of x² − 2xy + y² when x = 5 and y = 2.
14. 14.Find the value of x² − 2xy + y² when x = 3 and y = 1.
15. 15.Use (a + b)² = a² + 2ab + b² to find 103².
16. 16.Find the value of x² + 2xy + y² when x = 3 and y = 1.
17. 17.Use (a + b)(a − b) = a² − b² to find 49 × 31.
18. 18.Use a² − b² = (a + b)(a − b) to find 52² − 32².
19. 19.Use a² − b² = (a + b)(a − b) to find 77² − 68².
20. 20.Find the value of x² − y² when x = 13 and y = 5.
21. 21.If a + b = 8 and ab = 15, what is a² + b²?
22. 22.Use a² − b² = (a + b)(a − b) to find 50² − 15².
23. 23.Use (a − b)² = a² − 2ab + b² to find 14².
24. 24.Use (a + b)² = a² + 2ab + b² to find 64².
25. 25.Use (a + b)² = a² + 2ab + b² to find 31².
26. 26.Use (a + b)² = a² + 2ab + b² to find 25².
27. 27.Find the value of x² − 2xy + y² when x = 12 and y = 10.
28. 28.If a + b = 19 and ab = 90, what is a² + b²?
29. 29.Use a² − b² = (a + b)(a − b) to find 29² − 24².
30. 30.Use (a − b)² = a² − 2ab + b² to find 32².
31. 31.Use (a + b)² = a² + 2ab + b² to find 19².
32. 32.Use (a + b)² = a² + 2ab + b² to find 16².
33. 33.Use a² − b² = (a + b)(a − b) to find 79² − 66².
34. 34.Find the value of x² + 2xy + y² when x = 10 and y = 3.
35. 35.Use (a − b)² = a² − 2ab + b² to find 47².
36. 36.Find the value of x² + 2xy + y² when x = 10 and y = 8.
37. 37.Use (a + b)² = a² + 2ab + b² to find 44².
38. 38.If a − b = 1 and ab = 110, what is a² + b²?
39. 39.Find the value of x² + 2xy + y² when x = 7 and y = 6.
40. 40.Use a² − b² = (a + b)(a − b) to find 90² − 86².

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