Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 489 · 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.If a − b = 3 and ab = 70, what is a² + b²?
2. 2.If a + b = 13 and ab = 40, what is a² + b²?
3. 3.Use (a − b)² = a² − 2ab + b² to find 88².
4. 4.Use (a + b)² = a² + 2ab + b² to find 68².
5. 5.Use (a + b)(a − b) = a² − b² to find 99 × 81.
6. 6.Use a² − b² = (a + b)(a − b) to find 41² − 40².
7. 7.Use (a + b)(a − b) = a² − b² to find 49 × 31.
8. 8.Find the value of x² + 2xy + y² when x = 13 and y = 3.
9. 9.Use (a + b)(a − b) = a² − b² to find 52 × 48.
10. 10.If a − b = 3 and ab = 10, what is a² + b²?
11. 11.Find the value of x² + 2xy + y² when x = 4 and y = 2.
12. 12.Find the value of x² − 2xy + y² when x = 5 and y = 1.
13. 13.Use (a − b)² = a² − 2ab + b² to find 77².
14. 14.If a + b = 12 and ab = 32, what is a² + b²?
15. 15.Use (a + b)² = a² + 2ab + b² to find 48².
16. 16.If a + b = 5 and ab = 4, what is a² + b²?
17. 17.If a − b = 4 and ab = 5, what is a² + b²?
18. 18.If a − b = 2 and ab = 3, what is a² + b²?
19. 19.Use (a + b)² = a² + 2ab + b² to find 25².
20. 20.Use (a + b)(a − b) = a² − b² to find 43 × 37.
21. 21.Use a² − b² = (a + b)(a − b) to find 77² − 60².
22. 22.Use (a − b)² = a² − 2ab + b² to find 84².
23. 23.Use (a + b)² = a² + 2ab + b² to find 62².
24. 24.Find the value of x² − y² when x = 15 and y = 8.
25. 25.Use (a − b)² = a² − 2ab + b² to find 68².
26. 26.If a − b = 2 and ab = 15, what is a² + b²?
27. 27.If a − b = 7 and ab = 30, what is a² + b²?
28. 28.Use (a + b)² = a² + 2ab + b² to find 43².
29. 29.Use (a − b)² = a² − 2ab + b² to find 17².
30. 30.Use (a + b)² = a² + 2ab + b² to find 52².
31. 31.If a + b = 19 and ab = 88, what is a² + b²?
32. 32.Find the value of x² − 2xy + y² when x = 7 and y = 2.
33. 33.Use (a − b)² = a² − 2ab + b² to find 52².
34. 34.Use (a + b)(a − b) = a² − b² to find 33 × 27.
35. 35.Use a² − b² = (a + b)(a − b) to find 35² − 19².
36. 36.Use a² − b² = (a + b)(a − b) to find 56² − 22².
37. 37.If a − b = 1 and ab = 2, what is a² + b²?
38. 38.Use (a + b)(a − b) = a² − b² to find 41 × 39.
39. 39.Use (a + b)(a − b) = a² − b² to find 34 × 26.
40. 40.Use (a − b)² = a² − 2ab + b² to find 57².

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