Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 717 · 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 71² − 59².
2. 2.Use (a + b)(a − b) = a² − b² to find 29 × 11.
3. 3.Use (a + b)² = a² + 2ab + b² to find 18².
4. 4.Use (a + b)² = a² + 2ab + b² to find 89².
5. 5.Use (a + b)² = a² + 2ab + b² to find 26².
6. 6.Use a² − b² = (a + b)(a − b) to find 21² − 10².
7. 7.Find the value of x² + 2xy + y² when x = 5 and y = 2.
8. 8.If a + b = 15 and ab = 54, what is a² + b²?
9. 9.Use (a + b)² = a² + 2ab + b² to find 102².
10. 10.Use a² − b² = (a + b)(a − b) to find 30² − 8².
11. 11.Find the value of x² − 2xy + y² when x = 4 and y = 2.
12. 12.If a + b = 11 and ab = 30, what is a² + b²?
13. 13.Use (a + b)(a − b) = a² − b² to find 71 × 69.
14. 14.Use (a − b)² = a² − 2ab + b² to find 55².
15. 15.Use (a + b)² = a² + 2ab + b² to find 21².
16. 16.Use (a + b)(a − b) = a² − b² to find 94 × 86.
17. 17.Use (a + b)² = a² + 2ab + b² to find 19².
18. 18.Find the value of x² − 2xy + y² when x = 3 and y = 2.
19. 19.Use (a − b)² = a² − 2ab + b² to find 26².
20. 20.Use (a + b)(a − b) = a² − b² to find 39 × 21.
21. 21.Use (a + b)² = a² + 2ab + b² to find 47².
22. 22.Use (a + b)(a − b) = a² − b² to find 78 × 62.
23. 23.Use (a + b)² = a² + 2ab + b² to find 52².
24. 24.Use (a + b)(a − b) = a² − b² to find 35 × 25.
25. 25.Find the value of x² − y² when x = 9 and y = 1.
26. 26.If a + b = 11 and ab = 18, what is a² + b²?
27. 27.Use (a − b)² = a² − 2ab + b² to find 99².
28. 28.If a + b = 6 and ab = 5, what is a² + b²?
29. 29.Use a² − b² = (a + b)(a − b) to find 37² − 16².
30. 30.If a + b = 17 and ab = 60, what is a² + b²?
31. 31.Use (a − b)² = a² − 2ab + b² to find 47².
32. 32.Use (a − b)² = a² − 2ab + b² to find 74².
33. 33.If a − b = 2 and ab = 3, what is a² + b²?
34. 34.Use (a − b)² = a² − 2ab + b² to find 69².
35. 35.Use (a − b)² = a² − 2ab + b² to find 46².
36. 36.Use (a + b)² = a² + 2ab + b² to find 14².
37. 37.Find the value of x² + 2xy + y² when x = 11 and y = 10.
38. 38.Use (a − b)² = a² − 2ab + b² to find 65².
39. 39.Use (a − b)² = a² − 2ab + b² to find 37².
40. 40.If a + b = 5 and ab = 6, what is a² + b²?

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