Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 251 · 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 95².
2. 2.If a − b = 3 and ab = 108, what is a² + b²?
3. 3.Use (a + b)² = a² + 2ab + b² to find 47².
4. 4.Use (a − b)² = a² − 2ab + b² to find 89².
5. 5.Use (a + b)² = a² + 2ab + b² to find 83².
6. 6.Use (a − b)² = a² − 2ab + b² to find 17².
7. 7.Use (a − b)² = a² − 2ab + b² to find 44².
8. 8.Use (a + b)(a − b) = a² − b² to find 22 × 18.
9. 9.If a − b = 7 and ab = 30, what is a² + b²?
10. 10.Use a² − b² = (a + b)(a − b) to find 66² − 40².
11. 11.If a + b = 7 and ab = 6, what is a² + b²?
12. 12.Use a² − b² = (a + b)(a − b) to find 24² − 18².
13. 13.Find the value of x² − 2xy + y² when x = 10 and y = 7.
14. 14.Use (a + b)² = a² + 2ab + b² to find 28².
15. 15.Use (a − b)² = a² − 2ab + b² to find 93².
16. 16.Find the value of x² − y² when x = 12 and y = 6.
17. 17.Use (a + b)(a − b) = a² − b² to find 49 × 31.
18. 18.Use (a + b)(a − b) = a² − b² to find 54 × 46.
19. 19.Find the value of x² − 2xy + y² when x = 12 and y = 8.
20. 20.Find the value of x² − y² when x = 12 and y = 11.
21. 21.Use a² − b² = (a + b)(a − b) to find 22² − 6².
22. 22.Find the value of x² + 2xy + y² when x = 11 and y = 7.
23. 23.Use a² − b² = (a + b)(a − b) to find 76² − 44².
24. 24.Find the value of x² + 2xy + y² when x = 10 and y = 9.
25. 25.Use (a + b)(a − b) = a² − b² to find 32 × 28.
26. 26.Use (a + b)² = a² + 2ab + b² to find 85².
27. 27.Use a² − b² = (a + b)(a − b) to find 74² − 44².
28. 28.Use (a + b)² = a² + 2ab + b² to find 31².
29. 29.Find the value of x² − y² when x = 14 and y = 9.
30. 30.If a + b = 11 and ab = 28, what is a² + b²?
31. 31.Use (a + b)(a − b) = a² − b² to find 104 × 96.
32. 32.If a − b = 1 and ab = 12, what is a² + b²?
33. 33.Use (a + b)(a − b) = a² − b² to find 79 × 61.
34. 34.Use a² − b² = (a + b)(a − b) to find 94² − 11².
35. 35.Use (a − b)² = a² − 2ab + b² to find 98².
36. 36.Use (a + b)(a − b) = a² − b² to find 74 × 66.
37. 37.If a − b = 10 and ab = 11, what is a² + b²?
38. 38.If a + b = 10 and ab = 16, what is a² + b²?
39. 39.Use (a + b)(a − b) = a² − b² to find 84 × 76.
40. 40.Use a² − b² = (a + b)(a − b) to find 29² − 7².

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