Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 430 · 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)² = a² − 2ab + b² to find 79².
2. 2.Use (a + b)(a − b) = a² − b² to find 48 × 32.
3. 3.If a + b = 13 and ab = 42, what is a² + b²?
4. 4.Use a² − b² = (a + b)(a − b) to find 66² − 43².
5. 5.Use a² − b² = (a + b)(a − b) to find 23² − 10².
6. 6.Use (a − b)² = a² − 2ab + b² to find 29².
7. 7.Use (a + b)(a − b) = a² − b² to find 85 × 75.
8. 8.If a + b = 13 and ab = 30, what is a² + b²?
9. 9.Use (a − b)² = a² − 2ab + b² to find 34².
10. 10.Use (a − b)² = a² − 2ab + b² to find 25².
11. 11.Use (a + b)(a − b) = a² − b² to find 74 × 66.
12. 12.Find the value of x² + 2xy + y² when x = 15 and y = 1.
13. 13.Find the value of x² + 2xy + y² when x = 5 and y = 1.
14. 14.Find the value of x² − y² when x = 12 and y = 1.
15. 15.Use (a + b)² = a² + 2ab + b² to find 67².
16. 16.If a − b = 1 and ab = 12, what is a² + b²?
17. 17.Use (a − b)² = a² − 2ab + b² to find 53².
18. 18.Use (a − b)² = a² − 2ab + b² to find 56².
19. 19.Use (a − b)² = a² − 2ab + b² to find 59².
20. 20.Use (a + b)² = a² + 2ab + b² to find 14².
21. 21.If a + b = 14 and ab = 48, what is a² + b²?
22. 22.Use (a − b)² = a² − 2ab + b² to find 48².
23. 23.Use (a + b)² = a² + 2ab + b² to find 27².
24. 24.Find the value of x² + 2xy + y² when x = 7 and y = 6.
25. 25.Use (a + b)² = a² + 2ab + b² to find 79².
26. 26.Find the value of x² − y² when x = 10 and y = 2.
27. 27.Use (a + b)² = a² + 2ab + b² to find 38².
28. 28.If a + b = 21 and ab = 110, what is a² + b²?
29. 29.If a + b = 17 and ab = 70, what is a² + b²?
30. 30.Use (a − b)² = a² − 2ab + b² to find 37².
31. 31.Find the value of x² − 2xy + y² when x = 14 and y = 5.
32. 32.Use a² − b² = (a + b)(a − b) to find 61² − 15².
33. 33.Find the value of x² + 2xy + y² when x = 5 and y = 2.
34. 34.If a + b = 7 and ab = 12, what is a² + b²?
35. 35.Find the value of x² − y² when x = 4 and y = 3.
36. 36.Use (a + b)(a − b) = a² − b² to find 92 × 88.
37. 37.Use (a + b)² = a² + 2ab + b² to find 84².
38. 38.Use a² − b² = (a + b)(a − b) to find 30² − 14².
39. 39.Use a² − b² = (a + b)(a − b) to find 74² − 13².
40. 40.Use a² − b² = (a + b)(a − b) to find 27² − 4².

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