Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 572 · 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 67² − 11².
2. 2.Use (a + b)² = a² + 2ab + b² to find 59².
3. 3.Use (a − b)² = a² − 2ab + b² to find 94².
4. 4.Use (a + b)(a − b) = a² − b² to find 56 × 44.
5. 5.If a − b = 2 and ab = 120, what is a² + b²?
6. 6.Find the value of x² + 2xy + y² when x = 8 and y = 6.
7. 7.If a + b = 4 and ab = 3, what is a² + b²?
8. 8.Use (a − b)² = a² − 2ab + b² to find 28².
9. 9.If a − b = 1 and ab = 6, what is a² + b²?
10. 10.Use (a + b)(a − b) = a² − b² to find 106 × 94.
11. 11.Use (a + b)² = a² + 2ab + b² to find 41².
12. 12.Find the value of x² − 2xy + y² when x = 5 and y = 2.
13. 13.Use (a + b)² = a² + 2ab + b² to find 18².
14. 14.Use (a − b)² = a² − 2ab + b² to find 27².
15. 15.Find the value of x² + 2xy + y² when x = 3 and y = 2.
16. 16.Use a² − b² = (a + b)(a − b) to find 48² − 7².
17. 17.Use (a + b)(a − b) = a² − b² to find 68 × 52.
18. 18.Use (a + b)(a − b) = a² − b² to find 99 × 81.
19. 19.Use (a + b)² = a² + 2ab + b² to find 47².
20. 20.If a + b = 6 and ab = 8, what is a² + b²?
21. 21.Use (a − b)² = a² − 2ab + b² to find 26².
22. 22.If a − b = 4 and ab = 77, what is a² + b²?
23. 23.Find the value of x² + 2xy + y² when x = 9 and y = 6.
24. 24.Use (a − b)² = a² − 2ab + b² to find 18².
25. 25.Use (a + b)(a − b) = a² − b² to find 87 × 73.
26. 26.Use (a + b)² = a² + 2ab + b² to find 76².
27. 27.Use (a + b)(a − b) = a² − b² to find 84 × 76.
28. 28.Find the value of x² − y² when x = 5 and y = 4.
29. 29.Use (a − b)² = a² − 2ab + b² to find 43².
30. 30.Use (a + b)² = a² + 2ab + b² to find 69².
31. 31.Use (a − b)² = a² − 2ab + b² to find 61².
32. 32.Use (a − b)² = a² − 2ab + b² to find 67².
33. 33.Use (a − b)² = a² − 2ab + b² to find 13².
34. 34.Use (a + b)(a − b) = a² − b² to find 64 × 56.
35. 35.Use a² − b² = (a + b)(a − b) to find 37² − 31².
36. 36.Use (a − b)² = a² − 2ab + b² to find 74².
37. 37.Use (a + b)² = a² + 2ab + b² to find 99².
38. 38.Find the value of x² + 2xy + y² when x = 15 and y = 7.
39. 39.If a + b = 9 and ab = 20, what is a² + b²?
40. 40.Use (a + b)(a − b) = a² − b² to find 108 × 92.

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