Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 870 · 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 71².
2. 2.Find the value of x² − y² when x = 5 and y = 1.
3. 3.Find the value of x² + 2xy + y² when x = 12 and y = 1.
4. 4.Use a² − b² = (a + b)(a − b) to find 45² − 8².
5. 5.Use a² − b² = (a + b)(a − b) to find 63² − 54².
6. 6.Use (a + b)(a − b) = a² − b² to find 35 × 25.
7. 7.Use a² − b² = (a + b)(a − b) to find 46² − 36².
8. 8.Use (a + b)(a − b) = a² − b² to find 33 × 27.
9. 9.If a + b = 16 and ab = 48, what is a² + b²?
10. 10.If a − b = 1 and ab = 6, what is a² + b²?
11. 11.Use (a + b)² = a² + 2ab + b² to find 31².
12. 12.Use a² − b² = (a + b)(a − b) to find 22² − 1².
13. 13.Use (a + b)² = a² + 2ab + b² to find 32².
14. 14.Use a² − b² = (a + b)(a − b) to find 69² − 24².
15. 15.Use (a + b)(a − b) = a² − b² to find 73 × 67.
16. 16.Use (a − b)² = a² − 2ab + b² to find 78².
17. 17.Find the value of x² + 2xy + y² when x = 6 and y = 1.
18. 18.Use (a + b)² = a² + 2ab + b² to find 23².
19. 19.Use (a + b)(a − b) = a² − b² to find 31 × 29.
20. 20.Use (a + b)² = a² + 2ab + b² to find 85².
21. 21.Use (a + b)² = a² + 2ab + b² to find 25².
22. 22.Find the value of x² − y² when x = 4 and y = 2.
23. 23.Use (a − b)² = a² − 2ab + b² to find 62².
24. 24.Use a² − b² = (a + b)(a − b) to find 29² − 21².
25. 25.Use a² − b² = (a + b)(a − b) to find 51² − 14².
26. 26.Use (a + b)(a − b) = a² − b² to find 69 × 51.
27. 27.Find the value of x² + 2xy + y² when x = 11 and y = 9.
28. 28.Use (a − b)² = a² − 2ab + b² to find 65².
29. 29.Use (a + b)(a − b) = a² − b² to find 45 × 35.
30. 30.Use (a + b)(a − b) = a² − b² to find 52 × 48.
31. 31.Use (a + b)² = a² + 2ab + b² to find 34².
32. 32.If a + b = 7 and ab = 12, what is a² + b²?
33. 33.Use (a + b)(a − b) = a² − b² to find 53 × 47.
34. 34.Use (a − b)² = a² − 2ab + b² to find 67².
35. 35.If a − b = 6 and ab = 16, what is a² + b²?
36. 36.Find the value of x² − 2xy + y² when x = 4 and y = 2.
37. 37.Find the value of x² + 2xy + y² when x = 6 and y = 2.
38. 38.Use (a + b)² = a² + 2ab + b² to find 38².
39. 39.Use a² − b² = (a + b)(a − b) to find 24² − 12².
40. 40.Use (a + b)² = a² + 2ab + b² to find 35².

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