Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 769 · 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 69².
2. 2.Use (a − b)² = a² − 2ab + b² to find 91².
3. 3.Use (a − b)² = a² − 2ab + b² to find 53².
4. 4.If a + b = 14 and ab = 40, what is a² + b²?
5. 5.Find the value of x² − 2xy + y² when x = 8 and y = 4.
6. 6.Use (a + b)(a − b) = a² − b² to find 34 × 26.
7. 7.Find the value of x² − 2xy + y² when x = 7 and y = 6.
8. 8.Use (a + b)² = a² + 2ab + b² to find 35².
9. 9.Use (a − b)² = a² − 2ab + b² to find 68².
10. 10.If a − b = 5 and ab = 6, what is a² + b²?
11. 11.Use a² − b² = (a + b)(a − b) to find 81² − 10².
12. 12.Use (a + b)(a − b) = a² − b² to find 25 × 15.
13. 13.Use (a + b)(a − b) = a² − b² to find 96 × 84.
14. 14.Use (a + b)(a − b) = a² − b² to find 58 × 42.
15. 15.Find the value of x² − y² when x = 4 and y = 2.
16. 16.Find the value of x² − 2xy + y² when x = 14 and y = 10.
17. 17.Use (a + b)(a − b) = a² − b² to find 53 × 47.
18. 18.Use (a + b)(a − b) = a² − b² to find 44 × 36.
19. 19.Use (a + b)² = a² + 2ab + b² to find 62².
20. 20.Use (a − b)² = a² − 2ab + b² to find 92².
21. 21.Use (a + b)(a − b) = a² − b² to find 101 × 99.
22. 22.Use a² − b² = (a + b)(a − b) to find 91² − 43².
23. 23.If a − b = 4 and ab = 5, what is a² + b²?
24. 24.Use (a − b)² = a² − 2ab + b² to find 72².
25. 25.Use (a − b)² = a² − 2ab + b² to find 18².
26. 26.Use (a − b)² = a² − 2ab + b² to find 99².
27. 27.Find the value of x² + 2xy + y² when x = 9 and y = 5.
28. 28.Use (a − b)² = a² − 2ab + b² to find 33².
29. 29.Find the value of x² − y² when x = 9 and y = 4.
30. 30.Use (a − b)² = a² − 2ab + b² to find 77².
31. 31.Use (a + b)(a − b) = a² − b² to find 22 × 18.
32. 32.If a + b = 16 and ab = 48, what is a² + b²?
33. 33.Use (a + b)² = a² + 2ab + b² to find 33².
34. 34.Use (a − b)² = a² − 2ab + b² to find 23².
35. 35.Find the value of x² + 2xy + y² when x = 15 and y = 14.
36. 36.Use (a − b)² = a² − 2ab + b² to find 37².
37. 37.Use (a + b)² = a² + 2ab + b² to find 105².
38. 38.Use a² − b² = (a + b)(a − b) to find 62² − 35².
39. 39.Find the value of x² − y² when x = 12 and y = 10.
40. 40.Use a² − b² = (a + b)(a − b) to find 95² − 25².

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