Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 840 · 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 43².
2. 2.Use (a − b)² = a² − 2ab + b² to find 21².
3. 3.Use (a + b)(a − b) = a² − b² to find 109 × 91.
4. 4.Use (a + b)² = a² + 2ab + b² to find 106².
5. 5.Use (a − b)² = a² − 2ab + b² to find 84².
6. 6.If a − b = 1 and ab = 12, what is a² + b²?
7. 7.If a − b = 1 and ab = 2, what is a² + b²?
8. 8.Use (a + b)(a − b) = a² − b² to find 74 × 66.
9. 9.Use (a − b)² = a² − 2ab + b² to find 15².
10. 10.If a − b = 2 and ab = 48, what is a² + b²?
11. 11.Use a² − b² = (a + b)(a − b) to find 96² − 32².
12. 12.Use (a + b)² = a² + 2ab + b² to find 44².
13. 13.If a + b = 16 and ab = 48, what is a² + b²?
14. 14.Find the value of x² − 2xy + y² when x = 9 and y = 6.
15. 15.Find the value of x² − y² when x = 4 and y = 1.
16. 16.If a + b = 3 and ab = 2, what is a² + b²?
17. 17.Find the value of x² + 2xy + y² when x = 11 and y = 8.
18. 18.Use (a − b)² = a² − 2ab + b² to find 23².
19. 19.Find the value of x² + 2xy + y² when x = 11 and y = 6.
20. 20.Find the value of x² + 2xy + y² when x = 5 and y = 3.
21. 21.Use (a − b)² = a² − 2ab + b² to find 68².
22. 22.Find the value of x² + 2xy + y² when x = 6 and y = 1.
23. 23.Use (a + b)(a − b) = a² − b² to find 98 × 82.
24. 24.Use (a + b)² = a² + 2ab + b² to find 36².
25. 25.Use a² − b² = (a + b)(a − b) to find 76² − 57².
26. 26.Use (a − b)² = a² − 2ab + b² to find 39².
27. 27.Use (a + b)² = a² + 2ab + b² to find 23².
28. 28.Use a² − b² = (a + b)(a − b) to find 76² − 6².
29. 29.Use a² − b² = (a + b)(a − b) to find 56² − 10².
30. 30.Use (a + b)(a − b) = a² − b² to find 96 × 84.
31. 31.Use (a + b)² = a² + 2ab + b² to find 17².
32. 32.Use (a + b)(a − b) = a² − b² to find 97 × 83.
33. 33.Find the value of x² − 2xy + y² when x = 3 and y = 2.
34. 34.Find the value of x² + 2xy + y² when x = 3 and y = 2.
35. 35.Use (a − b)² = a² − 2ab + b² to find 89².
36. 36.Use (a − b)² = a² − 2ab + b² to find 12².
37. 37.Use (a − b)² = a² − 2ab + b² to find 34².
38. 38.Use (a + b)² = a² + 2ab + b² to find 24².
39. 39.Use a² − b² = (a + b)(a − b) to find 44² − 18².
40. 40.Use (a + b)² = a² + 2ab + b² to find 87².

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