Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 26 · 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 = 15 and y = 5.
2. 2.Use a² − b² = (a + b)(a − b) to find 36² − 2².
3. 3.If a + b = 7 and ab = 12, what is a² + b²?
4. 4.Use (a + b)(a − b) = a² − b² to find 71 × 69.
5. 5.Use (a + b)² = a² + 2ab + b² to find 88².
6. 6.Use (a − b)² = a² − 2ab + b² to find 87².
7. 7.Use (a − b)² = a² − 2ab + b² to find 56².
8. 8.Use (a + b)² = a² + 2ab + b² to find 21².
9. 9.Use a² − b² = (a + b)(a − b) to find 94² − 26².
10. 10.Use (a − b)² = a² − 2ab + b² to find 14².
11. 11.If a − b = 1 and ab = 72, what is a² + b²?
12. 12.If a − b = 9 and ab = 10, what is a² + b²?
13. 13.Use (a + b)(a − b) = a² − b² to find 38 × 22.
14. 14.Use (a − b)² = a² − 2ab + b² to find 24².
15. 15.Use (a + b)² = a² + 2ab + b² to find 81².
16. 16.Use (a − b)² = a² − 2ab + b² to find 46².
17. 17.Find the value of x² − 2xy + y² when x = 6 and y = 2.
18. 18.Use (a + b)² = a² + 2ab + b² to find 48².
19. 19.If a + b = 14 and ab = 40, what is a² + b²?
20. 20.Use (a − b)² = a² − 2ab + b² to find 92².
21. 21.Use a² − b² = (a + b)(a − b) to find 80² − 74².
22. 22.Find the value of x² − 2xy + y² when x = 13 and y = 6.
23. 23.Use (a + b)(a − b) = a² − b² to find 53 × 47.
24. 24.Find the value of x² − y² when x = 4 and y = 1.
25. 25.If a − b = 4 and ab = 5, what is a² + b²?
26. 26.Use a² − b² = (a + b)(a − b) to find 83² − 48².
27. 27.Find the value of x² + 2xy + y² when x = 4 and y = 2.
28. 28.Use a² − b² = (a + b)(a − b) to find 39² − 30².
29. 29.Find the value of x² + 2xy + y² when x = 10 and y = 3.
30. 30.Use (a − b)² = a² − 2ab + b² to find 98².
31. 31.Use (a + b)(a − b) = a² − b² to find 42 × 38.
32. 32.Use (a − b)² = a² − 2ab + b² to find 36².
33. 33.Use (a + b)² = a² + 2ab + b² to find 91².
34. 34.If a − b = 7 and ab = 18, what is a² + b²?
35. 35.If a + b = 13 and ab = 36, what is a² + b²?
36. 36.Use (a − b)² = a² − 2ab + b² to find 32².
37. 37.If a − b = 3 and ab = 10, what is a² + b²?
38. 38.Use (a − b)² = a² − 2ab + b² to find 33².
39. 39.Find the value of x² − y² when x = 10 and y = 4.
40. 40.If a + b = 5 and ab = 4, what is a² + b²?

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