Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 124 · 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)(a − b) = a² − b² to find 82 × 78.
2. 2.Find the value of x² − y² when x = 6 and y = 5.
3. 3.If a − b = 3 and ab = 70, what is a² + b²?
4. 4.Use (a + b)(a − b) = a² − b² to find 47 × 33.
5. 5.Use (a − b)² = a² − 2ab + b² to find 92².
6. 6.Use (a + b)(a − b) = a² − b² to find 75 × 65.
7. 7.Use (a + b)² = a² + 2ab + b² to find 21².
8. 8.Use (a + b)² = a² + 2ab + b² to find 74².
9. 9.Use a² − b² = (a + b)(a − b) to find 23² − 9².
10. 10.Use (a + b)² = a² + 2ab + b² to find 33².
11. 11.Use (a + b)² = a² + 2ab + b² to find 37².
12. 12.Use (a + b)² = a² + 2ab + b² to find 83².
13. 13.Use (a − b)² = a² − 2ab + b² to find 27².
14. 14.Find the value of x² − 2xy + y² when x = 8 and y = 3.
15. 15.If a + b = 4 and ab = 3, what is a² + b²?
16. 16.Use (a + b)(a − b) = a² − b² to find 44 × 36.
17. 17.Use (a + b)(a − b) = a² − b² to find 45 × 35.
18. 18.Use (a − b)² = a² − 2ab + b² to find 45².
19. 19.Find the value of x² − y² when x = 4 and y = 1.
20. 20.Find the value of x² − 2xy + y² when x = 8 and y = 1.
21. 21.Use a² − b² = (a + b)(a − b) to find 28² − 13².
22. 22.Find the value of x² − y² when x = 11 and y = 7.
23. 23.Find the value of x² − y² when x = 14 and y = 5.
24. 24.Use a² − b² = (a + b)(a − b) to find 33² − 26².
25. 25.Use (a − b)² = a² − 2ab + b² to find 46².
26. 26.Find the value of x² + 2xy + y² when x = 14 and y = 6.
27. 27.Use (a − b)² = a² − 2ab + b² to find 32².
28. 28.Use (a − b)² = a² − 2ab + b² to find 89².
29. 29.Use (a − b)² = a² − 2ab + b² to find 91².
30. 30.Use (a − b)² = a² − 2ab + b² to find 47².
31. 31.Use (a + b)² = a² + 2ab + b² to find 88².
32. 32.Use (a + b)² = a² + 2ab + b² to find 87².
33. 33.Use a² − b² = (a + b)(a − b) to find 92² − 45².
34. 34.If a − b = 8 and ab = 9, what is a² + b²?
35. 35.If a − b = 7 and ab = 8, what is a² + b²?
36. 36.Use (a − b)² = a² − 2ab + b² to find 54².
37. 37.Use (a + b)(a − b) = a² − b² to find 66 × 54.
38. 38.Find the value of x² − y² when x = 10 and y = 6.
39. 39.If a + b = 17 and ab = 70, what is a² + b²?
40. 40.If a + b = 11 and ab = 10, what is a² + b²?

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