Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 545 · 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 54².
2. 2.Use (a + b)(a − b) = a² − b² to find 87 × 73.
3. 3.Use a² − b² = (a + b)(a − b) to find 56² − 45².
4. 4.Use a² − b² = (a + b)(a − b) to find 27² − 2².
5. 5.Use a² − b² = (a + b)(a − b) to find 67² − 12².
6. 6.Use a² − b² = (a + b)(a − b) to find 97² − 11².
7. 7.Find the value of x² − 2xy + y² when x = 10 and y = 9.
8. 8.Use (a + b)(a − b) = a² − b² to find 44 × 36.
9. 9.Use (a + b)(a − b) = a² − b² to find 92 × 88.
10. 10.Use (a + b)(a − b) = a² − b² to find 64 × 56.
11. 11.Use a² − b² = (a + b)(a − b) to find 70² − 32².
12. 12.If a + b = 13 and ab = 40, what is a² + b²?
13. 13.Use (a − b)² = a² − 2ab + b² to find 91².
14. 14.If a − b = 4 and ab = 5, what is a² + b²?
15. 15.Find the value of x² + 2xy + y² when x = 7 and y = 6.
16. 16.Find the value of x² + 2xy + y² when x = 13 and y = 11.
17. 17.Use (a + b)(a − b) = a² − b² to find 48 × 32.
18. 18.Use (a − b)² = a² − 2ab + b² to find 56².
19. 19.Use (a + b)² = a² + 2ab + b² to find 102².
20. 20.Find the value of x² − y² when x = 13 and y = 2.
21. 21.Use (a − b)² = a² − 2ab + b² to find 49².
22. 22.Use a² − b² = (a + b)(a − b) to find 24² − 11².
23. 23.Find the value of x² + 2xy + y² when x = 11 and y = 3.
24. 24.Use (a + b)² = a² + 2ab + b² to find 41².
25. 25.Use (a + b)² = a² + 2ab + b² to find 27².
26. 26.If a + b = 4 and ab = 3, what is a² + b²?
27. 27.Find the value of x² + 2xy + y² when x = 8 and y = 4.
28. 28.Use a² − b² = (a + b)(a − b) to find 81² − 1².
29. 29.If a + b = 6 and ab = 8, what is a² + b²?
30. 30.Use a² − b² = (a + b)(a − b) to find 89² − 25².
31. 31.Use (a + b)² = a² + 2ab + b² to find 44².
32. 32.Use (a + b)² = a² + 2ab + b² to find 33².
33. 33.Use (a + b)² = a² + 2ab + b² to find 22².
34. 34.Use (a + b)² = a² + 2ab + b² to find 67².
35. 35.Use (a − b)² = a² − 2ab + b² to find 43².
36. 36.Use (a + b)(a − b) = a² − b² to find 69 × 51.
37. 37.Use a² − b² = (a + b)(a − b) to find 40² − 18².
38. 38.Use (a + b)(a − b) = a² − b² to find 43 × 37.
39. 39.Use (a + b)² = a² + 2ab + b² to find 92².
40. 40.Use (a + b)(a − b) = a² − b² to find 51 × 49.

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