Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 444 · 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.Find the value of x² − y² when x = 3 and y = 1.
2. 2.Use a² − b² = (a + b)(a − b) to find 50² − 4².
3. 3.If a + b = 17 and ab = 66, what is a² + b²?
4. 4.If a − b = 1 and ab = 2, what is a² + b²?
5. 5.Find the value of x² − 2xy + y² when x = 6 and y = 2.
6. 6.If a − b = 5 and ab = 6, what is a² + b²?
7. 7.Use (a + b)(a − b) = a² − b² to find 22 × 18.
8. 8.Use (a − b)² = a² − 2ab + b² to find 69².
9. 9.If a + b = 6 and ab = 5, what is a² + b²?
10. 10.Use (a + b)² = a² + 2ab + b² to find 102².
11. 11.Use (a + b)² = a² + 2ab + b² to find 103².
12. 12.Use a² − b² = (a + b)(a − b) to find 83² − 51².
13. 13.Use (a − b)² = a² − 2ab + b² to find 31².
14. 14.Find the value of x² − 2xy + y² when x = 11 and y = 9.
15. 15.Use (a + b)(a − b) = a² − b² to find 32 × 28.
16. 16.Use (a + b)² = a² + 2ab + b² to find 46².
17. 17.Use a² − b² = (a + b)(a − b) to find 76² − 43².
18. 18.Find the value of x² − y² when x = 5 and y = 1.
19. 19.Use (a − b)² = a² − 2ab + b² to find 74².
20. 20.Use (a + b)(a − b) = a² − b² to find 72 × 68.
21. 21.Use (a + b)² = a² + 2ab + b² to find 92².
22. 22.Use (a + b)(a − b) = a² − b² to find 59 × 41.
23. 23.Find the value of x² + 2xy + y² when x = 4 and y = 1.
24. 24.If a + b = 15 and ab = 44, what is a² + b²?
25. 25.Find the value of x² + 2xy + y² when x = 7 and y = 5.
26. 26.Use a² − b² = (a + b)(a − b) to find 33² − 12².
27. 27.Use (a + b)(a − b) = a² − b² to find 33 × 27.
28. 28.Use (a + b)² = a² + 2ab + b² to find 25².
29. 29.Use (a + b)(a − b) = a² − b² to find 26 × 14.
30. 30.Use (a + b)(a − b) = a² − b² to find 42 × 38.
31. 31.Use (a − b)² = a² − 2ab + b² to find 34².
32. 32.Find the value of x² − y² when x = 6 and y = 2.
33. 33.Use (a + b)² = a² + 2ab + b² to find 58².
34. 34.Use (a + b)² = a² + 2ab + b² to find 77².
35. 35.Use (a + b)² = a² + 2ab + b² to find 88².
36. 36.Use (a + b)(a − b) = a² − b² to find 34 × 26.
37. 37.If a + b = 14 and ab = 40, what is a² + b²?
38. 38.If a − b = 2 and ab = 3, what is a² + b²?
39. 39.If a + b = 7 and ab = 12, what is a² + b²?
40. 40.Use (a + b)² = a² + 2ab + b² to find 22².

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