Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 460 · 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 32 × 28.
2. 2.Use (a − b)² = a² − 2ab + b² to find 88².
3. 3.Use a² − b² = (a + b)(a − b) to find 60² − 59².
4. 4.Use a² − b² = (a + b)(a − b) to find 44² − 10².
5. 5.Find the value of x² − y² when x = 12 and y = 2.
6. 6.Find the value of x² − y² when x = 10 and y = 4.
7. 7.Use (a − b)² = a² − 2ab + b² to find 12².
8. 8.Use (a − b)² = a² − 2ab + b² to find 13².
9. 9.Use (a − b)² = a² − 2ab + b² to find 26².
10. 10.Use (a + b)(a − b) = a² − b² to find 72 × 68.
11. 11.Use (a + b)(a − b) = a² − b² to find 25 × 15.
12. 12.Use (a − b)² = a² − 2ab + b² to find 17².
13. 13.Use (a − b)² = a² − 2ab + b² to find 16².
14. 14.Use (a + b)² = a² + 2ab + b² to find 74².
15. 15.Use a² − b² = (a + b)(a − b) to find 30² − 23².
16. 16.Use (a + b)(a − b) = a² − b² to find 44 × 36.
17. 17.Use (a + b)² = a² + 2ab + b² to find 91².
18. 18.Use (a + b)² = a² + 2ab + b² to find 88².
19. 19.Find the value of x² + 2xy + y² when x = 3 and y = 1.
20. 20.Use a² − b² = (a + b)(a − b) to find 29² − 20².
21. 21.If a − b = 1 and ab = 2, what is a² + b²?
22. 22.Find the value of x² + 2xy + y² when x = 6 and y = 3.
23. 23.Find the value of x² − y² when x = 7 and y = 2.
24. 24.Use (a − b)² = a² − 2ab + b² to find 37².
25. 25.Use (a + b)² = a² + 2ab + b² to find 24².
26. 26.Use (a − b)² = a² − 2ab + b² to find 24².
27. 27.If a + b = 6 and ab = 5, what is a² + b²?
28. 28.If a + b = 4 and ab = 3, what is a² + b²?
29. 29.Find the value of x² + 2xy + y² when x = 5 and y = 2.
30. 30.Use a² − b² = (a + b)(a − b) to find 94² − 10².
31. 31.Use (a + b)(a − b) = a² − b² to find 76 × 64.
32. 32.If a − b = 2 and ab = 3, what is a² + b²?
33. 33.Find the value of x² + 2xy + y² when x = 11 and y = 9.
34. 34.Use (a + b)² = a² + 2ab + b² to find 43².
35. 35.Use (a + b)(a − b) = a² − b² to find 29 × 11.
36. 36.Use (a + b)² = a² + 2ab + b² to find 32².
37. 37.Use (a − b)² = a² − 2ab + b² to find 89².
38. 38.Use a² − b² = (a + b)(a − b) to find 43² − 8².
39. 39.Use (a + b)(a − b) = a² − b² to find 27 × 13.
40. 40.Use (a − b)² = a² − 2ab + b² to find 63².

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