Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 232 · 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 (a + b)² = a² + 2ab + b² to find 46².
2. 2.Use (a − b)² = a² − 2ab + b² to find 48².
3. 3.Use (a + b)² = a² + 2ab + b² to find 43².
4. 4.Find the value of x² − 2xy + y² when x = 9 and y = 2.
5. 5.Use (a − b)² = a² − 2ab + b² to find 93².
6. 6.Use (a + b)² = a² + 2ab + b² to find 45².
7. 7.If a + b = 7 and ab = 12, what is a² + b²?
8. 8.Use a² − b² = (a + b)(a − b) to find 48² − 36².
9. 9.Use (a + b)(a − b) = a² − b² to find 28 × 12.
10. 10.Use a² − b² = (a + b)(a − b) to find 57² − 10².
11. 11.Use (a − b)² = a² − 2ab + b² to find 42².
12. 12.If a − b = 3 and ab = 54, what is a² + b²?
13. 13.If a + b = 9 and ab = 14, what is a² + b²?
14. 14.If a − b = 3 and ab = 4, what is a² + b²?
15. 15.Use (a − b)² = a² − 2ab + b² to find 26².
16. 16.Use (a − b)² = a² − 2ab + b² to find 27².
17. 17.Use (a + b)(a − b) = a² − b² to find 34 × 26.
18. 18.If a + b = 10 and ab = 24, what is a² + b²?
19. 19.Use (a + b)² = a² + 2ab + b² to find 54².
20. 20.Find the value of x² − y² when x = 12 and y = 1.
21. 21.If a − b = 7 and ab = 30, what is a² + b²?
22. 22.Use (a + b)(a − b) = a² − b² to find 72 × 68.
23. 23.Use (a − b)² = a² − 2ab + b² to find 57².
24. 24.Use (a + b)(a − b) = a² − b² to find 56 × 44.
25. 25.Find the value of x² − y² when x = 6 and y = 1.
26. 26.Use (a + b)(a − b) = a² − b² to find 76 × 64.
27. 27.Find the value of x² + 2xy + y² when x = 5 and y = 4.
28. 28.If a − b = 2 and ab = 80, what is a² + b²?
29. 29.Use (a + b)² = a² + 2ab + b² to find 49².
30. 30.Use a² − b² = (a + b)(a − b) to find 37² − 15².
31. 31.Use a² − b² = (a + b)(a − b) to find 26² − 1².
32. 32.Use (a + b)² = a² + 2ab + b² to find 16².
33. 33.Use a² − b² = (a + b)(a − b) to find 22² − 14².
34. 34.Use (a + b)² = a² + 2ab + b² to find 48².
35. 35.If a + b = 16 and ab = 48, what is a² + b²?
36. 36.Find the value of x² + 2xy + y² when x = 13 and y = 4.
37. 37.Use (a − b)² = a² − 2ab + b² to find 31².
38. 38.Find the value of x² + 2xy + y² when x = 8 and y = 5.
39. 39.Use a² − b² = (a + b)(a − b) to find 39² − 8².
40. 40.Find the value of x² − 2xy + y² when x = 15 and y = 7.

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