Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 321 · 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 28².
2. 2.Use (a − b)² = a² − 2ab + b² to find 99².
3. 3.Use (a − b)² = a² − 2ab + b² to find 68².
4. 4.Find the value of x² + 2xy + y² when x = 5 and y = 3.
5. 5.If a + b = 14 and ab = 45, what is a² + b²?
6. 6.Use (a + b)² = a² + 2ab + b² to find 103².
7. 7.Use (a + b)(a − b) = a² − b² to find 24 × 16.
8. 8.Use a² − b² = (a + b)(a − b) to find 48² − 1².
9. 9.Find the value of x² − 2xy + y² when x = 11 and y = 2.
10. 10.Use a² − b² = (a + b)(a − b) to find 53² − 30².
11. 11.Use (a + b)² = a² + 2ab + b² to find 18².
12. 12.Use (a + b)(a − b) = a² − b² to find 52 × 48.
13. 13.Find the value of x² − y² when x = 5 and y = 3.
14. 14.Use (a + b)² = a² + 2ab + b² to find 54².
15. 15.Use (a − b)² = a² − 2ab + b² to find 89².
16. 16.Use (a + b)(a − b) = a² − b² to find 87 × 73.
17. 17.If a − b = 4 and ab = 5, what is a² + b²?
18. 18.Use (a − b)² = a² − 2ab + b² to find 69².
19. 19.Find the value of x² + 2xy + y² when x = 10 and y = 8.
20. 20.Use (a − b)² = a² − 2ab + b² to find 61².
21. 21.Use (a + b)² = a² + 2ab + b² to find 108².
22. 22.Find the value of x² − 2xy + y² when x = 5 and y = 1.
23. 23.Find the value of x² − 2xy + y² when x = 3 and y = 2.
24. 24.Find the value of x² − 2xy + y² when x = 8 and y = 4.
25. 25.Use (a − b)² = a² − 2ab + b² to find 51².
26. 26.Use (a + b)(a − b) = a² − b² to find 58 × 42.
27. 27.If a + b = 8 and ab = 15, what is a² + b²?
28. 28.Use (a + b)(a − b) = a² − b² to find 59 × 41.
29. 29.Use (a − b)² = a² − 2ab + b² to find 79².
30. 30.Use a² − b² = (a + b)(a − b) to find 38² − 18².
31. 31.Use (a + b)² = a² + 2ab + b² to find 97².
32. 32.Use a² − b² = (a + b)(a − b) to find 66² − 47².
33. 33.If a + b = 10 and ab = 21, what is a² + b²?
34. 34.Use (a + b)² = a² + 2ab + b² to find 25².
35. 35.Use a² − b² = (a + b)(a − b) to find 72² − 32².
36. 36.Use (a + b)² = a² + 2ab + b² to find 14².
37. 37.Use a² − b² = (a + b)(a − b) to find 26² − 4².
38. 38.Find the value of x² − 2xy + y² when x = 12 and y = 6.
39. 39.Use (a − b)² = a² − 2ab + b² to find 58².
40. 40.Use (a + b)(a − b) = a² − b² to find 23 × 17.

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