Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 813 · 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 a² − b² = (a + b)(a − b) to find 27² − 3².
2. 2.Use a² − b² = (a + b)(a − b) to find 51² − 36².
3. 3.Find the value of x² + 2xy + y² when x = 4 and y = 1.
4. 4.Use (a + b)² = a² + 2ab + b² to find 21².
5. 5.Use (a − b)² = a² − 2ab + b² to find 21².
6. 6.Use a² − b² = (a + b)(a − b) to find 40² − 37².
7. 7.Find the value of x² + 2xy + y² when x = 13 and y = 6.
8. 8.Find the value of x² − 2xy + y² when x = 11 and y = 2.
9. 9.Use (a + b)(a − b) = a² − b² to find 21 × 19.
10. 10.Use (a + b)² = a² + 2ab + b² to find 52².
11. 11.Use (a + b)(a − b) = a² − b² to find 33 × 27.
12. 12.If a + b = 9 and ab = 8, what is a² + b²?
13. 13.Find the value of x² − 2xy + y² when x = 4 and y = 3.
14. 14.Use (a + b)(a − b) = a² − b² to find 27 × 13.
15. 15.If a + b = 9 and ab = 18, what is a² + b²?
16. 16.Use (a + b)(a − b) = a² − b² to find 78 × 62.
17. 17.Find the value of x² − 2xy + y² when x = 7 and y = 3.
18. 18.Use (a + b)² = a² + 2ab + b² to find 32².
19. 19.If a + b = 15 and ab = 36, what is a² + b²?
20. 20.Use a² − b² = (a + b)(a − b) to find 56² − 1².
21. 21.Find the value of x² − 2xy + y² when x = 12 and y = 5.
22. 22.Find the value of x² − 2xy + y² when x = 3 and y = 1.
23. 23.Use (a − b)² = a² − 2ab + b² to find 54².
24. 24.Use (a − b)² = a² − 2ab + b² to find 77².
25. 25.Use (a + b)² = a² + 2ab + b² to find 87².
26. 26.Find the value of x² − y² when x = 11 and y = 4.
27. 27.If a + b = 6 and ab = 8, what is a² + b²?
28. 28.Find the value of x² + 2xy + y² when x = 5 and y = 2.
29. 29.Use a² − b² = (a + b)(a − b) to find 38² − 13².
30. 30.Use (a + b)² = a² + 2ab + b² to find 42².
31. 31.Use (a − b)² = a² − 2ab + b² to find 67².
32. 32.If a + b = 6 and ab = 5, what is a² + b²?
33. 33.Use a² − b² = (a + b)(a − b) to find 69² − 64².
34. 34.Use (a + b)² = a² + 2ab + b² to find 35².
35. 35.Find the value of x² − y² when x = 13 and y = 11.
36. 36.Use (a − b)² = a² − 2ab + b² to find 84².
37. 37.Use (a + b)(a − b) = a² − b² to find 94 × 86.
38. 38.Find the value of x² − 2xy + y² when x = 5 and y = 1.
39. 39.If a − b = 1 and ab = 20, what is a² + b²?
40. 40.Find the value of x² − 2xy + y² when x = 8 and y = 1.

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