Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 759 · 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 = 5 and ab = 6, what is a² + b²?
2. 2.If a − b = 1 and ab = 56, what is a² + b²?
3. 3.Use a² − b² = (a + b)(a − b) to find 73² − 1².
4. 4.Use (a + b)² = a² + 2ab + b² to find 18².
5. 5.Use a² − b² = (a + b)(a − b) to find 69² − 3².
6. 6.If a + b = 10 and ab = 24, what is a² + b²?
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 = 5.
9. 9.Use (a − b)² = a² − 2ab + b² to find 34².
10. 10.Use a² − b² = (a + b)(a − b) to find 32² − 30².
11. 11.Use (a − b)² = a² − 2ab + b² to find 69².
12. 12.Use (a + b)² = a² + 2ab + b² to find 16².
13. 13.Use (a + b)² = a² + 2ab + b² to find 31².
14. 14.If a + b = 6 and ab = 8, what is a² + b²?
15. 15.Use (a + b)² = a² + 2ab + b² to find 38².
16. 16.Use (a + b)² = a² + 2ab + b² to find 23².
17. 17.Use (a + b)(a − b) = a² − b² to find 59 × 41.
18. 18.Use (a + b)² = a² + 2ab + b² to find 91².
19. 19.Find the value of x² + 2xy + y² when x = 14 and y = 1.
20. 20.Use (a − b)² = a² − 2ab + b² to find 49².
21. 21.Use (a + b)(a − b) = a² − b² to find 107 × 93.
22. 22.Use (a + b)(a − b) = a² − b² to find 84 × 76.
23. 23.Find the value of x² + 2xy + y² when x = 4 and y = 1.
24. 24.Use (a − b)² = a² − 2ab + b² to find 21².
25. 25.Use a² − b² = (a + b)(a − b) to find 24² − 10².
26. 26.Find the value of x² + 2xy + y² when x = 11 and y = 4.
27. 27.Use (a + b)(a − b) = a² − b² to find 106 × 94.
28. 28.Find the value of x² − y² when x = 14 and y = 3.
29. 29.Use a² − b² = (a + b)(a − b) to find 30² − 10².
30. 30.Use (a + b)² = a² + 2ab + b² to find 82².
31. 31.Use a² − b² = (a + b)(a − b) to find 74² − 49².
32. 32.Use (a + b)² = a² + 2ab + b² to find 69².
33. 33.Use (a + b)(a − b) = a² − b² to find 79 × 61.
34. 34.Use (a + b)(a − b) = a² − b² to find 102 × 98.
35. 35.Use (a − b)² = a² − 2ab + b² to find 22².
36. 36.Use (a + b)(a − b) = a² − b² to find 29 × 11.
37. 37.Use a² − b² = (a + b)(a − b) to find 89² − 6².
38. 38.If a + b = 8 and ab = 7, what is a² + b²?
39. 39.If a − b = 2 and ab = 3, what is a² + b²?
40. 40.Find the value of x² − 2xy + y² when x = 4 and y = 3.

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