Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 805 · 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.Find the value of x² − y² when x = 8 and y = 1.
2. 2.Use (a + b)² = a² + 2ab + b² to find 42².
3. 3.Use (a − b)² = a² − 2ab + b² to find 23².
4. 4.Use (a + b)² = a² + 2ab + b² to find 28².
5. 5.Find the value of x² − 2xy + y² when x = 7 and y = 2.
6. 6.Use a² − b² = (a + b)(a − b) to find 22² − 8².
7. 7.If a − b = 4 and ab = 21, what is a² + b²?
8. 8.Find the value of x² + 2xy + y² when x = 8 and y = 1.
9. 9.If a − b = 2 and ab = 15, what is a² + b²?
10. 10.Use (a + b)² = a² + 2ab + b² to find 78².
11. 11.Use (a + b)² = a² + 2ab + b² to find 33².
12. 12.Find the value of x² + 2xy + y² when x = 5 and y = 1.
13. 13.Use (a − b)² = a² − 2ab + b² to find 87².
14. 14.Use (a + b)(a − b) = a² − b² to find 87 × 73.
15. 15.Find the value of x² − y² when x = 11 and y = 10.
16. 16.Use (a + b)(a − b) = a² − b² to find 38 × 22.
17. 17.Use a² − b² = (a + b)(a − b) to find 84² − 66².
18. 18.Use a² − b² = (a + b)(a − b) to find 50² − 18².
19. 19.Use a² − b² = (a + b)(a − b) to find 76² − 1².
20. 20.Find the value of x² − 2xy + y² when x = 10 and y = 4.
21. 21.Use a² − b² = (a + b)(a − b) to find 63² − 34².
22. 22.Use (a + b)(a − b) = a² − b² to find 95 × 85.
23. 23.Find the value of x² + 2xy + y² when x = 7 and y = 1.
24. 24.Use (a + b)² = a² + 2ab + b² to find 56².
25. 25.If a + b = 13 and ab = 36, what is a² + b²?
26. 26.Use a² − b² = (a + b)(a − b) to find 40² − 19².
27. 27.Use a² − b² = (a + b)(a − b) to find 52² − 25².
28. 28.If a + b = 8 and ab = 15, what is a² + b²?
29. 29.Find the value of x² − y² when x = 8 and y = 7.
30. 30.Use (a + b)² = a² + 2ab + b² to find 84².
31. 31.If a − b = 2 and ab = 48, what is a² + b²?
32. 32.Use a² − b² = (a + b)(a − b) to find 66² − 17².
33. 33.Use (a + b)² = a² + 2ab + b² to find 62².
34. 34.If a + b = 5 and ab = 4, what is a² + b²?
35. 35.Use a² − b² = (a + b)(a − b) to find 49² − 27².
36. 36.Use (a − b)² = a² − 2ab + b² to find 78².
37. 37.Use (a + b)(a − b) = a² − b² to find 101 × 99.
38. 38.Find the value of x² − y² when x = 3 and y = 1.
39. 39.Use (a + b)² = a² + 2ab + b² to find 55².
40. 40.Use (a + b)² = a² + 2ab + b² to find 29².

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