Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 657 · 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 = 7 and ab = 10, what is a² + b²?
2. 2.Use (a − b)² = a² − 2ab + b² to find 59².
3. 3.If a + b = 9 and ab = 18, what is a² + b²?
4. 4.Use (a + b)(a − b) = a² − b² to find 34 × 26.
5. 5.If a − b = 1 and ab = 2, what is a² + b²?
6. 6.Use (a + b)² = a² + 2ab + b² to find 62².
7. 7.Find the value of x² − 2xy + y² when x = 6 and y = 3.
8. 8.Use (a + b)(a − b) = a² − b² to find 84 × 76.
9. 9.Find the value of x² − y² when x = 5 and y = 2.
10. 10.If a + b = 17 and ab = 72, what is a² + b²?
11. 11.Find the value of x² − y² when x = 6 and y = 3.
12. 12.Find the value of x² + 2xy + y² when x = 3 and y = 1.
13. 13.Use a² − b² = (a + b)(a − b) to find 42² − 17².
14. 14.Use (a − b)² = a² − 2ab + b² to find 77².
15. 15.Use (a − b)² = a² − 2ab + b² to find 85².
16. 16.If a + b = 13 and ab = 36, what is a² + b²?
17. 17.Use (a + b)² = a² + 2ab + b² to find 49².
18. 18.Use (a − b)² = a² − 2ab + b² to find 46².
19. 19.If a − b = 1 and ab = 30, what is a² + b²?
20. 20.Use (a − b)² = a² − 2ab + b² to find 11².
21. 21.Use (a + b)² = a² + 2ab + b² to find 84².
22. 22.Use (a + b)² = a² + 2ab + b² to find 77².
23. 23.Use (a − b)² = a² − 2ab + b² to find 14².
24. 24.Use a² − b² = (a + b)(a − b) to find 52² − 37².
25. 25.Use (a − b)² = a² − 2ab + b² to find 21².
26. 26.If a − b = 6 and ab = 55, what is a² + b²?
27. 27.Use a² − b² = (a + b)(a − b) to find 29² − 12².
28. 28.Find the value of x² + 2xy + y² when x = 11 and y = 6.
29. 29.Use (a + b)² = a² + 2ab + b² to find 48².
30. 30.Use (a + b)(a − b) = a² − b² to find 101 × 99.
31. 31.Use (a + b)(a − b) = a² − b² to find 35 × 25.
32. 32.Use (a − b)² = a² − 2ab + b² to find 28².
33. 33.Use a² − b² = (a + b)(a − b) to find 23² − 2².
34. 34.If a − b = 3 and ab = 28, what is a² + b²?
35. 35.Use (a + b)(a − b) = a² − b² to find 66 × 54.
36. 36.Use a² − b² = (a + b)(a − b) to find 29² − 27².
37. 37.Use a² − b² = (a + b)(a − b) to find 47² − 33².
38. 38.Find the value of x² − 2xy + y² when x = 11 and y = 9.
39. 39.Use a² − b² = (a + b)(a − b) to find 89² − 74².
40. 40.Use (a + b)² = a² + 2ab + b² to find 13².

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