Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 889 · 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 30² − 12².
2. 2.Find the value of x² − 2xy + y² when x = 3 and y = 1.
3. 3.Use (a + b)² = a² + 2ab + b² to find 69².
4. 4.Find the value of x² − y² when x = 10 and y = 2.
5. 5.Use (a − b)² = a² − 2ab + b² to find 57².
6. 6.Find the value of x² − y² when x = 9 and y = 8.
7. 7.Use (a + b)² = a² + 2ab + b² to find 26².
8. 8.Use (a + b)(a − b) = a² − b² to find 68 × 52.
9. 9.Use (a − b)² = a² − 2ab + b² to find 53².
10. 10.Use (a − b)² = a² − 2ab + b² to find 25².
11. 11.Use (a − b)² = a² − 2ab + b² to find 18².
12. 12.If a − b = 6 and ab = 72, what is a² + b²?
13. 13.Use (a − b)² = a² − 2ab + b² to find 17².
14. 14.Use (a + b)² = a² + 2ab + b² to find 32².
15. 15.Use (a − b)² = a² − 2ab + b² to find 65².
16. 16.Use a² − b² = (a + b)(a − b) to find 77² − 4².
17. 17.Use (a + b)(a − b) = a² − b² to find 73 × 67.
18. 18.Use (a + b)² = a² + 2ab + b² to find 18².
19. 19.Use a² − b² = (a + b)(a − b) to find 59² − 28².
20. 20.Use (a + b)² = a² + 2ab + b² to find 15².
21. 21.Use (a − b)² = a² − 2ab + b² to find 91².
22. 22.Use a² − b² = (a + b)(a − b) to find 63² − 50².
23. 23.Use (a + b)² = a² + 2ab + b² to find 43².
24. 24.Find the value of x² − 2xy + y² when x = 6 and y = 4.
25. 25.If a + b = 14 and ab = 40, what is a² + b²?
26. 26.Use (a + b)(a − b) = a² − b² to find 106 × 94.
27. 27.Use (a − b)² = a² − 2ab + b² to find 26².
28. 28.Use (a + b)² = a² + 2ab + b² to find 44².
29. 29.Use a² − b² = (a + b)(a − b) to find 91² − 69².
30. 30.Find the value of x² − 2xy + y² when x = 6 and y = 5.
31. 31.Use (a − b)² = a² − 2ab + b² to find 54².
32. 32.Use (a + b)² = a² + 2ab + b² to find 14².
33. 33.Find the value of x² − y² when x = 12 and y = 3.
34. 34.Find the value of x² + 2xy + y² when x = 9 and y = 2.
35. 35.Use (a + b)(a − b) = a² − b² to find 91 × 89.
36. 36.Use (a + b)(a − b) = a² − b² to find 89 × 71.
37. 37.Use a² − b² = (a + b)(a − b) to find 52² − 27².
38. 38.Use (a + b)(a − b) = a² − b² to find 65 × 55.
39. 39.If a + b = 3 and ab = 2, what is a² + b²?
40. 40.If a + b = 6 and ab = 5, what is a² + b²?

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