Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 445 · 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 = 13 and ab = 40, what is a² + b²?
2. 2.Find the value of x² − y² when x = 3 and y = 2.
3. 3.Use (a + b)² = a² + 2ab + b² to find 87².
4. 4.Find the value of x² + 2xy + y² when x = 7 and y = 4.
5. 5.Use (a + b)(a − b) = a² − b² to find 51 × 49.
6. 6.Use (a + b)² = a² + 2ab + b² to find 23².
7. 7.Use a² − b² = (a + b)(a − b) to find 61² − 7².
8. 8.Use (a + b)(a − b) = a² − b² to find 82 × 78.
9. 9.If a + b = 3 and ab = 2, what is a² + b²?
10. 10.Use (a + b)² = a² + 2ab + b² to find 67².
11. 11.If a − b = 5 and ab = 6, what is a² + b²?
12. 12.Use (a + b)(a − b) = a² − b² to find 92 × 88.
13. 13.Use (a − b)² = a² − 2ab + b² to find 65².
14. 14.Use (a + b)(a − b) = a² − b² to find 28 × 12.
15. 15.Use a² − b² = (a + b)(a − b) to find 89² − 57².
16. 16.Use (a + b)(a − b) = a² − b² to find 21 × 19.
17. 17.Use (a + b)² = a² + 2ab + b² to find 102².
18. 18.Use a² − b² = (a + b)(a − b) to find 44² − 34².
19. 19.If a + b = 12 and ab = 27, what is a² + b²?
20. 20.Use a² − b² = (a + b)(a − b) to find 24² − 3².
21. 21.Find the value of x² + 2xy + y² when x = 9 and y = 5.
22. 22.Use (a + b)² = a² + 2ab + b² to find 21².
23. 23.Find the value of x² + 2xy + y² when x = 8 and y = 5.
24. 24.Use (a − b)² = a² − 2ab + b² to find 81².
25. 25.If a + b = 22 and ab = 120, what is a² + b²?
26. 26.Use (a + b)(a − b) = a² − b² to find 22 × 18.
27. 27.Use a² − b² = (a + b)(a − b) to find 75² − 55².
28. 28.Use (a + b)(a − b) = a² − b² to find 104 × 96.
29. 29.Use (a + b)² = a² + 2ab + b² to find 39².
30. 30.If a − b = 1 and ab = 90, what is a² + b²?
31. 31.Use (a + b)² = a² + 2ab + b² to find 36².
32. 32.Use (a + b)(a − b) = a² − b² to find 101 × 99.
33. 33.If a − b = 1 and ab = 12, what is a² + b²?
34. 34.Use (a + b)² = a² + 2ab + b² to find 71².
35. 35.If a − b = 2 and ab = 15, what is a² + b²?
36. 36.Use (a − b)² = a² − 2ab + b² to find 26².
37. 37.Find the value of x² − 2xy + y² when x = 6 and y = 1.
38. 38.Find the value of x² − y² when x = 5 and y = 1.
39. 39.Find the value of x² + 2xy + y² when x = 4 and y = 1.
40. 40.Use a² − b² = (a + b)(a − b) to find 57² − 49².

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