Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 552 · 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 a² − b² = (a + b)(a − b) to find 40² − 1².
2. 2.Use (a + b)² = a² + 2ab + b² to find 42².
3. 3.Use (a + b)(a − b) = a² − b² to find 105 × 95.
4. 4.If a + b = 7 and ab = 10, what is a² + b²?
5. 5.Use (a + b)(a − b) = a² − b² to find 35 × 25.
6. 6.If a − b = 3 and ab = 40, what is a² + b²?
7. 7.If a − b = 2 and ab = 8, what is a² + b²?
8. 8.Use (a − b)² = a² − 2ab + b² to find 19².
9. 9.Use a² − b² = (a + b)(a − b) to find 35² − 28².
10. 10.Find the value of x² + 2xy + y² when x = 15 and y = 2.
11. 11.Use (a − b)² = a² − 2ab + b² to find 88².
12. 12.Find the value of x² − y² when x = 13 and y = 9.
13. 13.If a − b = 1 and ab = 12, what is a² + b²?
14. 14.Use a² − b² = (a + b)(a − b) to find 98² − 80².
15. 15.Use (a + b)(a − b) = a² − b² to find 94 × 86.
16. 16.Use (a + b)² = a² + 2ab + b² to find 49².
17. 17.Use (a + b)² = a² + 2ab + b² to find 24².
18. 18.Find the value of x² − 2xy + y² when x = 7 and y = 1.
19. 19.Use (a − b)² = a² − 2ab + b² to find 11².
20. 20.Use (a − b)² = a² − 2ab + b² to find 67².
21. 21.Use (a + b)(a − b) = a² − b² to find 42 × 38.
22. 22.Use (a + b)(a − b) = a² − b² to find 106 × 94.
23. 23.If a − b = 4 and ab = 12, what is a² + b²?
24. 24.Use (a − b)² = a² − 2ab + b² to find 95².
25. 25.If a − b = 1 and ab = 6, what is a² + b²?
26. 26.Use (a + b)(a − b) = a² − b² to find 62 × 58.
27. 27.Use (a + b)(a − b) = a² − b² to find 96 × 84.
28. 28.Find the value of x² − 2xy + y² when x = 13 and y = 10.
29. 29.If a − b = 3 and ab = 108, what is a² + b²?
30. 30.Use (a − b)² = a² − 2ab + b² to find 93².
31. 31.Use (a + b)² = a² + 2ab + b² to find 102².
32. 32.Use a² − b² = (a + b)(a − b) to find 59² − 48².
33. 33.Use (a − b)² = a² − 2ab + b² to find 52².
34. 34.If a − b = 1 and ab = 110, what is a² + b²?
35. 35.Use (a + b)(a − b) = a² − b² to find 55 × 45.
36. 36.Use (a − b)² = a² − 2ab + b² to find 21².
37. 37.Use a² − b² = (a + b)(a − b) to find 91² − 16².
38. 38.Use (a − b)² = a² − 2ab + b² to find 92².
39. 39.Use (a + b)² = a² + 2ab + b² to find 38².
40. 40.Find the value of x² − 2xy + y² when x = 7 and y = 6.

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