Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 34 · 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.Find the value of x² − y² when x = 8 and y = 3.
2. 2.Find the value of x² − 2xy + y² when x = 5 and y = 4.
3. 3.If a + b = 6 and ab = 8, what is a² + b²?
4. 4.Find the value of x² + 2xy + y² when x = 10 and y = 1.
5. 5.Use (a + b)(a − b) = a² − b² to find 35 × 25.
6. 6.Use (a + b)(a − b) = a² − b² to find 81 × 79.
7. 7.Use (a + b)² = a² + 2ab + b² to find 14².
8. 8.Use (a + b)(a − b) = a² − b² to find 61 × 59.
9. 9.Use a² − b² = (a + b)(a − b) to find 94² − 75².
10. 10.Use (a − b)² = a² − 2ab + b² to find 37².
11. 11.If a − b = 3 and ab = 70, what is a² + b²?
12. 12.If a + b = 5 and ab = 6, what is a² + b²?
13. 13.Use (a − b)² = a² − 2ab + b² to find 99².
14. 14.Use (a + b)² = a² + 2ab + b² to find 88².
15. 15.Use (a + b)² = a² + 2ab + b² to find 35².
16. 16.Use (a − b)² = a² − 2ab + b² to find 81².
17. 17.Use a² − b² = (a + b)(a − b) to find 91² − 55².
18. 18.If a + b = 3 and ab = 2, what is a² + b²?
19. 19.Use a² − b² = (a + b)(a − b) to find 22² − 17².
20. 20.Use (a + b)² = a² + 2ab + b² to find 18².
21. 21.Use a² − b² = (a + b)(a − b) to find 51² − 47².
22. 22.Use (a + b)(a − b) = a² − b² to find 78 × 62.
23. 23.Use (a + b)² = a² + 2ab + b² to find 44².
24. 24.Find the value of x² − 2xy + y² when x = 6 and y = 1.
25. 25.If a − b = 1 and ab = 2, what is a² + b²?
26. 26.Use (a − b)² = a² − 2ab + b² to find 72².
27. 27.Use (a − b)² = a² − 2ab + b² to find 78².
28. 28.Use (a + b)² = a² + 2ab + b² to find 77².
29. 29.Use (a + b)(a − b) = a² − b² to find 31 × 29.
30. 30.Use (a − b)² = a² − 2ab + b² to find 31².
31. 31.Find the value of x² + 2xy + y² when x = 11 and y = 4.
32. 32.Find the value of x² − y² when x = 11 and y = 10.
33. 33.Use a² − b² = (a + b)(a − b) to find 58² − 28².
34. 34.Use a² − b² = (a + b)(a − b) to find 51² − 6².
35. 35.Use (a − b)² = a² − 2ab + b² to find 84².
36. 36.Find the value of x² − y² when x = 10 and y = 9.
37. 37.Use (a + b)(a − b) = a² − b² to find 48 × 32.
38. 38.Use (a − b)² = a² − 2ab + b² to find 75².
39. 39.Use a² − b² = (a + b)(a − b) to find 60² − 2².
40. 40.Use (a + b)² = a² + 2ab + b² to find 68².

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