Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 987 · 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 = 7 and y = 2.
2. 2.Use (a − b)² = a² − 2ab + b² to find 78².
3. 3.Use (a − b)² = a² − 2ab + b² to find 79².
4. 4.If a − b = 3 and ab = 18, what is a² + b²?
5. 5.Use a² − b² = (a + b)(a − b) to find 36² − 4².
6. 6.Use a² − b² = (a + b)(a − b) to find 73² − 36².
7. 7.Use (a + b)(a − b) = a² − b² to find 92 × 88.
8. 8.Use (a + b)² = a² + 2ab + b² to find 17².
9. 9.If a − b = 5 and ab = 14, what is a² + b²?
10. 10.Use (a + b)(a − b) = a² − b² to find 103 × 97.
11. 11.If a − b = 3 and ab = 28, what is a² + b²?
12. 12.Find the value of x² − 2xy + y² when x = 3 and y = 2.
13. 13.Find the value of x² − y² when x = 6 and y = 1.
14. 14.Use (a + b)(a − b) = a² − b² to find 22 × 18.
15. 15.Use (a + b)(a − b) = a² − b² to find 45 × 35.
16. 16.Use a² − b² = (a + b)(a − b) to find 84² − 48².
17. 17.Use (a + b)(a − b) = a² − b² to find 107 × 93.
18. 18.Use (a + b)² = a² + 2ab + b² to find 33².
19. 19.If a − b = 1 and ab = 90, what is a² + b²?
20. 20.Find the value of x² + 2xy + y² when x = 5 and y = 3.
21. 21.Use (a + b)(a − b) = a² − b² to find 35 × 25.
22. 22.Use (a − b)² = a² − 2ab + b² to find 38².
23. 23.Use (a + b)² = a² + 2ab + b² to find 38².
24. 24.If a + b = 10 and ab = 21, what is a² + b²?
25. 25.Use (a + b)(a − b) = a² − b² to find 36 × 24.
26. 26.Use (a + b)² = a² + 2ab + b² to find 13².
27. 27.If a + b = 13 and ab = 30, what is a² + b²?
28. 28.Use (a + b)(a − b) = a² − b² to find 89 × 71.
29. 29.Use (a − b)² = a² − 2ab + b² to find 61².
30. 30.Find the value of x² + 2xy + y² when x = 6 and y = 2.
31. 31.Use a² − b² = (a + b)(a − b) to find 72² − 1².
32. 32.Use (a + b)² = a² + 2ab + b² to find 68².
33. 33.Use a² − b² = (a + b)(a − b) to find 64² − 11².
34. 34.Use a² − b² = (a + b)(a − b) to find 35² − 9².
35. 35.If a − b = 6 and ab = 40, what is a² + b²?
36. 36.If a − b = 6 and ab = 55, what is a² + b²?
37. 37.Use (a + b)² = a² + 2ab + b² to find 21².
38. 38.Use (a − b)² = a² − 2ab + b² to find 95².
39. 39.Use a² − b² = (a + b)(a − b) to find 78² − 23².
40. 40.Find the value of x² + 2xy + y² when x = 3 and y = 2.

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