Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 477 · 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 = 7 and y = 1.
2. 2.If a − b = 11 and ab = 12, what is a² + b²?
3. 3.Find the value of x² − y² when x = 13 and y = 5.
4. 4.Use (a − b)² = a² − 2ab + b² to find 91².
5. 5.Find the value of x² + 2xy + y² when x = 6 and y = 3.
6. 6.Find the value of x² − 2xy + y² when x = 8 and y = 1.
7. 7.Find the value of x² − y² when x = 9 and y = 1.
8. 8.Use a² − b² = (a + b)(a − b) to find 22² − 2².
9. 9.Use (a + b)² = a² + 2ab + b² to find 27².
10. 10.Use a² − b² = (a + b)(a − b) to find 71² − 21².
11. 11.Find the value of x² − y² when x = 7 and y = 5.
12. 12.Use (a − b)² = a² − 2ab + b² to find 94².
13. 13.Use (a − b)² = a² − 2ab + b² to find 26².
14. 14.Use (a − b)² = a² − 2ab + b² to find 86².
15. 15.Use (a − b)² = a² − 2ab + b² to find 79².
16. 16.Use (a − b)² = a² − 2ab + b² to find 65².
17. 17.Use (a + b)(a − b) = a² − b² to find 35 × 25.
18. 18.Use (a + b)(a − b) = a² − b² to find 41 × 39.
19. 19.Use (a − b)² = a² − 2ab + b² to find 57².
20. 20.If a − b = 9 and ab = 36, what is a² + b²?
21. 21.Use a² − b² = (a + b)(a − b) to find 32² − 8².
22. 22.Use a² − b² = (a + b)(a − b) to find 61² − 37².
23. 23.Use (a + b)² = a² + 2ab + b² to find 94².
24. 24.Use (a + b)² = a² + 2ab + b² to find 21².
25. 25.Use a² − b² = (a + b)(a − b) to find 20² − 19².
26. 26.Use (a + b)² = a² + 2ab + b² to find 93².
27. 27.Use (a + b)(a − b) = a² − b² to find 52 × 48.
28. 28.Find the value of x² + 2xy + y² when x = 8 and y = 2.
29. 29.Use (a + b)(a − b) = a² − b² to find 101 × 99.
30. 30.Use (a + b)² = a² + 2ab + b² to find 89².
31. 31.Find the value of x² + 2xy + y² when x = 6 and y = 2.
32. 32.Find the value of x² + 2xy + y² when x = 11 and y = 1.
33. 33.If a − b = 1 and ab = 12, what is a² + b²?
34. 34.Use (a + b)² = a² + 2ab + b² to find 14².
35. 35.Find the value of x² + 2xy + y² when x = 4 and y = 2.
36. 36.Use (a + b)(a − b) = a² − b² to find 89 × 71.
37. 37.Use (a + b)(a − b) = a² − b² to find 25 × 15.
38. 38.If a − b = 1 and ab = 72, what is a² + b²?
39. 39.Find the value of x² − 2xy + y² when x = 6 and y = 1.
40. 40.If a + b = 4 and ab = 3, what is a² + b²?

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