Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 94 · 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 33².
2. 2.Find the value of x² + 2xy + y² when x = 15 and y = 6.
3. 3.Use a² − b² = (a + b)(a − b) to find 51² − 24².
4. 4.Use (a + b)(a − b) = a² − b² to find 72 × 68.
5. 5.Use (a + b)(a − b) = a² − b² to find 37 × 23.
6. 6.Use a² − b² = (a + b)(a − b) to find 98² − 77².
7. 7.If a − b = 2 and ab = 8, what is a² + b²?
8. 8.Use a² − b² = (a + b)(a − b) to find 61² − 8².
9. 9.If a − b = 7 and ab = 8, what is a² + b²?
10. 10.Find the value of x² − 2xy + y² when x = 6 and y = 5.
11. 11.Use (a + b)² = a² + 2ab + b² to find 54².
12. 12.Use a² − b² = (a + b)(a − b) to find 91² − 31².
13. 13.Use (a + b)² = a² + 2ab + b² to find 79².
14. 14.If a + b = 8 and ab = 15, what is a² + b²?
15. 15.Find the value of x² + 2xy + y² when x = 12 and y = 7.
16. 16.Use (a + b)² = a² + 2ab + b² to find 77².
17. 17.If a − b = 1 and ab = 42, what is a² + b²?
18. 18.Use (a − b)² = a² − 2ab + b² to find 27².
19. 19.If a − b = 1 and ab = 56, what is a² + b²?
20. 20.Use (a + b)(a − b) = a² − b² to find 98 × 82.
21. 21.Use (a + b)(a − b) = a² − b² to find 35 × 25.
22. 22.Use (a − b)² = a² − 2ab + b² to find 82².
23. 23.Find the value of x² − 2xy + y² when x = 15 and y = 5.
24. 24.Use (a − b)² = a² − 2ab + b² to find 39².
25. 25.Use (a + b)² = a² + 2ab + b² to find 21².
26. 26.Use (a + b)² = a² + 2ab + b² to find 78².
27. 27.If a − b = 5 and ab = 24, what is a² + b²?
28. 28.Use (a + b)(a − b) = a² − b² to find 67 × 53.
29. 29.Use (a − b)² = a² − 2ab + b² to find 58².
30. 30.Find the value of x² + 2xy + y² when x = 7 and y = 3.
31. 31.Find the value of x² − y² when x = 7 and y = 6.
32. 32.Use (a − b)² = a² − 2ab + b² to find 42².
33. 33.Use (a + b)² = a² + 2ab + b² to find 41².
34. 34.Use a² − b² = (a + b)(a − b) to find 55² − 11².
35. 35.Use (a − b)² = a² − 2ab + b² to find 63².
36. 36.If a − b = 6 and ab = 27, what is a² + b²?
37. 37.Use (a + b)(a − b) = a² − b² to find 104 × 96.
38. 38.If a − b = 4 and ab = 5, what is a² + b²?
39. 39.Find the value of x² + 2xy + y² when x = 10 and y = 3.
40. 40.Use (a − b)² = a² − 2ab + b² to find 53².

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