Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 496 · 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)(a − b) = a² − b² to find 21 × 19.
2. 2.Use (a + b)(a − b) = a² − b² to find 58 × 42.
3. 3.Use a² − b² = (a + b)(a − b) to find 88² − 74².
4. 4.Use (a − b)² = a² − 2ab + b² to find 97².
5. 5.Use (a + b)(a − b) = a² − b² to find 92 × 88.
6. 6.Use (a + b)² = a² + 2ab + b² to find 43².
7. 7.Use (a − b)² = a² − 2ab + b² to find 87².
8. 8.Find the value of x² + 2xy + y² when x = 7 and y = 2.
9. 9.Use (a + b)² = a² + 2ab + b² to find 38².
10. 10.Use (a + b)² = a² + 2ab + b² to find 71².
11. 11.Use (a + b)² = a² + 2ab + b² to find 13².
12. 12.Use (a + b)² = a² + 2ab + b² to find 66².
13. 13.Use a² − b² = (a + b)(a − b) to find 53² − 6².
14. 14.If a + b = 3 and ab = 2, what is a² + b²?
15. 15.Use (a + b)(a − b) = a² − b² to find 22 × 18.
16. 16.Find the value of x² − 2xy + y² when x = 6 and y = 4.
17. 17.Use (a + b)(a − b) = a² − b² to find 45 × 35.
18. 18.Use (a + b)² = a² + 2ab + b² to find 15².
19. 19.If a + b = 7 and ab = 10, what is a² + b²?
20. 20.Use (a + b)² = a² + 2ab + b² to find 101².
21. 21.Use (a − b)² = a² − 2ab + b² to find 42².
22. 22.Use (a + b)² = a² + 2ab + b² to find 11².
23. 23.Use (a + b)(a − b) = a² − b² to find 65 × 55.
24. 24.Use a² − b² = (a + b)(a − b) to find 40² − 13².
25. 25.If a − b = 3 and ab = 4, what is a² + b²?
26. 26.Use (a + b)² = a² + 2ab + b² to find 23².
27. 27.Use (a + b)² = a² + 2ab + b² to find 22².
28. 28.Use (a + b)² = a² + 2ab + b² to find 61².
29. 29.Use (a + b)(a − b) = a² − b² to find 54 × 46.
30. 30.Use (a − b)² = a² − 2ab + b² to find 33².
31. 31.Find the value of x² − 2xy + y² when x = 7 and y = 1.
32. 32.If a − b = 1 and ab = 72, what is a² + b²?
33. 33.Use (a + b)(a − b) = a² − b² to find 88 × 72.
34. 34.Use a² − b² = (a + b)(a − b) to find 39² − 25².
35. 35.Find the value of x² + 2xy + y² when x = 8 and y = 6.
36. 36.If a − b = 2 and ab = 3, what is a² + b²?
37. 37.If a − b = 1 and ab = 56, what is a² + b²?
38. 38.Use (a + b)(a − b) = a² − b² to find 44 × 36.
39. 39.Find the value of x² − 2xy + y² when x = 4 and y = 3.
40. 40.Use (a − b)² = a² − 2ab + b² to find 38².

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