Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 449 · 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.If a + b = 5 and ab = 4, what is a² + b²?
2. 2.If a + b = 15 and ab = 50, what is a² + b²?
3. 3.Use (a + b)² = a² + 2ab + b² to find 46².
4. 4.Use (a + b)² = a² + 2ab + b² to find 72².
5. 5.Use (a + b)² = a² + 2ab + b² to find 37².
6. 6.Use (a + b)(a − b) = a² − b² to find 48 × 32.
7. 7.Use (a − b)² = a² − 2ab + b² to find 38².
8. 8.Use (a + b)² = a² + 2ab + b² to find 26².
9. 9.Find the value of x² − y² when x = 11 and y = 3.
10. 10.Use a² − b² = (a + b)(a − b) to find 91² − 88².
11. 11.Use (a − b)² = a² − 2ab + b² to find 54².
12. 12.Find the value of x² − 2xy + y² when x = 12 and y = 7.
13. 13.Find the value of x² − 2xy + y² when x = 15 and y = 14.
14. 14.Use a² − b² = (a + b)(a − b) to find 52² − 31².
15. 15.If a + b = 13 and ab = 36, what is a² + b²?
16. 16.Use a² − b² = (a + b)(a − b) to find 50² − 16².
17. 17.Use a² − b² = (a + b)(a − b) to find 25² − 13².
18. 18.Find the value of x² − 2xy + y² when x = 4 and y = 1.
19. 19.If a − b = 3 and ab = 4, what is a² + b²?
20. 20.Use (a + b)(a − b) = a² − b² to find 36 × 24.
21. 21.Use a² − b² = (a + b)(a − b) to find 27² − 7².
22. 22.If a − b = 1 and ab = 2, what is a² + b²?
23. 23.Use (a − b)² = a² − 2ab + b² to find 43².
24. 24.Use (a + b)² = a² + 2ab + b² to find 12².
25. 25.Use (a + b)² = a² + 2ab + b² to find 77².
26. 26.Find the value of x² + 2xy + y² when x = 13 and y = 9.
27. 27.Use (a + b)² = a² + 2ab + b² to find 78².
28. 28.Use (a + b)² = a² + 2ab + b² to find 57².
29. 29.Use (a + b)² = a² + 2ab + b² to find 93².
30. 30.Use (a + b)² = a² + 2ab + b² to find 13².
31. 31.Use (a + b)(a − b) = a² − b² to find 69 × 51.
32. 32.Use (a + b)² = a² + 2ab + b² to find 42².
33. 33.Find the value of x² − 2xy + y² when x = 10 and y = 1.
34. 34.Find the value of x² − y² when x = 9 and y = 5.
35. 35.Use a² − b² = (a + b)(a − b) to find 90² − 44².
36. 36.Use (a + b)(a − b) = a² − b² to find 32 × 28.
37. 37.Use (a + b)² = a² + 2ab + b² to find 89².
38. 38.Find the value of x² + 2xy + y² when x = 10 and y = 1.
39. 39.Find the value of x² − y² when x = 9 and y = 1.
40. 40.Use (a − b)² = a² − 2ab + b² to find 21².

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