Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 947 · 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.Find the value of x² + 2xy + y² when x = 4 and y = 1.
2. 2.Use (a + b)(a − b) = a² − b² to find 62 × 58.
3. 3.Use (a + b)² = a² + 2ab + b² to find 65².
4. 4.Use (a − b)² = a² − 2ab + b² to find 86².
5. 5.Use a² − b² = (a + b)(a − b) to find 30² − 9².
6. 6.If a − b = 1 and ab = 30, what is a² + b²?
7. 7.If a − b = 1 and ab = 20, what is a² + b²?
8. 8.Use (a − b)² = a² − 2ab + b² to find 95².
9. 9.Use a² − b² = (a + b)(a − b) to find 57² − 11².
10. 10.Find the value of x² + 2xy + y² when x = 6 and y = 2.
11. 11.Find the value of x² − y² when x = 5 and y = 3.
12. 12.If a − b = 5 and ab = 24, what is a² + b²?
13. 13.Find the value of x² + 2xy + y² when x = 9 and y = 5.
14. 14.Use (a − b)² = a² − 2ab + b² to find 84².
15. 15.Use (a + b)² = a² + 2ab + b² to find 72².
16. 16.Use (a + b)² = a² + 2ab + b² to find 82².
17. 17.Use (a + b)² = a² + 2ab + b² to find 92².
18. 18.Use (a + b)² = a² + 2ab + b² to find 94².
19. 19.Use a² − b² = (a + b)(a − b) to find 87² − 55².
20. 20.Use (a + b)(a − b) = a² − b² to find 67 × 53.
21. 21.Use (a + b)(a − b) = a² − b² to find 66 × 54.
22. 22.If a + b = 9 and ab = 20, what is a² + b²?
23. 23.Use (a + b)(a − b) = a² − b² to find 33 × 27.
24. 24.Use (a + b)² = a² + 2ab + b² to find 32².
25. 25.If a − b = 2 and ab = 48, what is a² + b²?
26. 26.Use (a + b)² = a² + 2ab + b² to find 42².
27. 27.Use (a + b)² = a² + 2ab + b² to find 73².
28. 28.Use a² − b² = (a + b)(a − b) to find 36² − 32².
29. 29.Use (a + b)(a − b) = a² − b² to find 107 × 93.
30. 30.Use (a + b)(a − b) = a² − b² to find 37 × 23.
31. 31.Use (a + b)(a − b) = a² − b² to find 76 × 64.
32. 32.Use (a − b)² = a² − 2ab + b² to find 89².
33. 33.Use a² − b² = (a + b)(a − b) to find 76² − 75².
34. 34.Use (a + b)(a − b) = a² − b² to find 106 × 94.
35. 35.Use a² − b² = (a + b)(a − b) to find 90² − 77².
36. 36.Use (a − b)² = a² − 2ab + b² to find 11².
37. 37.Use (a + b)(a − b) = a² − b² to find 87 × 73.
38. 38.Use (a + b)(a − b) = a² − b² to find 28 × 12.
39. 39.Use (a − b)² = a² − 2ab + b² to find 94².
40. 40.Use a² − b² = (a + b)(a − b) to find 95² − 42².

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