Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 664 · 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 51² − 24².
2. 2.Use (a + b)² = a² + 2ab + b² to find 25².
3. 3.Find the value of x² + 2xy + y² when x = 7 and y = 3.
4. 4.If a − b = 2 and ab = 3, what is a² + b²?
5. 5.Find the value of x² − 2xy + y² when x = 4 and y = 3.
6. 6.Find the value of x² − y² when x = 12 and y = 11.
7. 7.Use (a + b)(a − b) = a² − b² to find 66 × 54.
8. 8.Use (a − b)² = a² − 2ab + b² to find 18².
9. 9.Use (a + b)² = a² + 2ab + b² to find 63².
10. 10.Use (a + b)(a − b) = a² − b² to find 43 × 37.
11. 11.If a − b = 9 and ab = 36, what is a² + b²?
12. 12.Use a² − b² = (a + b)(a − b) to find 38² − 37².
13. 13.Find the value of x² + 2xy + y² when x = 8 and y = 7.
14. 14.If a + b = 4 and ab = 3, what is a² + b²?
15. 15.Find the value of x² − 2xy + y² when x = 8 and y = 1.
16. 16.Use (a − b)² = a² − 2ab + b² to find 91².
17. 17.Find the value of x² + 2xy + y² when x = 3 and y = 2.
18. 18.Use (a + b)(a − b) = a² − b² to find 88 × 72.
19. 19.Use (a + b)² = a² + 2ab + b² to find 106².
20. 20.Find the value of x² − 2xy + y² when x = 3 and y = 2.
21. 21.Find the value of x² + 2xy + y² when x = 11 and y = 10.
22. 22.Use (a + b)(a − b) = a² − b² to find 83 × 77.
23. 23.Use (a − b)² = a² − 2ab + b² to find 65².
24. 24.Use a² − b² = (a + b)(a − b) to find 76² − 40².
25. 25.Use (a + b)(a − b) = a² − b² to find 78 × 62.
26. 26.Find the value of x² − 2xy + y² when x = 6 and y = 3.
27. 27.Find the value of x² − 2xy + y² when x = 3 and y = 1.
28. 28.Use a² − b² = (a + b)(a − b) to find 79² − 72².
29. 29.Find the value of x² − y² when x = 8 and y = 2.
30. 30.Use (a + b)(a − b) = a² − b² to find 104 × 96.
31. 31.Use a² − b² = (a + b)(a − b) to find 98² − 20².
32. 32.Use (a + b)(a − b) = a² − b² to find 86 × 74.
33. 33.Use (a − b)² = a² − 2ab + b² to find 15².
34. 34.Find the value of x² − 2xy + y² when x = 10 and y = 1.
35. 35.Find the value of x² + 2xy + y² when x = 10 and y = 2.
36. 36.If a + b = 14 and ab = 40, what is a² + b²?
37. 37.Use (a + b)² = a² + 2ab + b² to find 31².
38. 38.Find the value of x² − 2xy + y² when x = 15 and y = 5.
39. 39.Use (a + b)(a − b) = a² − b² to find 97 × 83.
40. 40.Use (a − b)² = a² − 2ab + b² to find 23².

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