Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 815 · 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.If a + b = 13 and ab = 36, what is a² + b²?
2. 2.Use a² − b² = (a + b)(a − b) to find 48² − 7².
3. 3.Use (a + b)(a − b) = a² − b² to find 109 × 91.
4. 4.If a + b = 4 and ab = 3, what is a² + b²?
5. 5.Use (a − b)² = a² − 2ab + b² to find 23².
6. 6.Use (a − b)² = a² − 2ab + b² to find 79².
7. 7.If a − b = 4 and ab = 21, what is a² + b²?
8. 8.Use a² − b² = (a + b)(a − b) to find 52² − 24².
9. 9.Use (a − b)² = a² − 2ab + b² to find 48².
10. 10.Use (a − b)² = a² − 2ab + b² to find 99².
11. 11.If a − b = 3 and ab = 4, what is a² + b²?
12. 12.Find the value of x² − y² when x = 4 and y = 1.
13. 13.Use (a − b)² = a² − 2ab + b² to find 47².
14. 14.Use (a + b)² = a² + 2ab + b² to find 48².
15. 15.Use (a + b)² = a² + 2ab + b² to find 21².
16. 16.If a + b = 8 and ab = 7, what is a² + b²?
17. 17.Find the value of x² − 2xy + y² when x = 9 and y = 7.
18. 18.Use (a + b)(a − b) = a² − b² to find 76 × 64.
19. 19.Use a² − b² = (a + b)(a − b) to find 40² − 36².
20. 20.Use (a − b)² = a² − 2ab + b² to find 82².
21. 21.Use (a + b)² = a² + 2ab + b² to find 109².
22. 22.Find the value of x² − y² when x = 3 and y = 2.
23. 23.If a − b = 3 and ab = 18, what is a² + b²?
24. 24.Find the value of x² − 2xy + y² when x = 5 and y = 2.
25. 25.Use (a + b)² = a² + 2ab + b² to find 93².
26. 26.Use (a + b)(a − b) = a² − b² to find 108 × 92.
27. 27.Use (a + b)(a − b) = a² − b² to find 74 × 66.
28. 28.If a − b = 7 and ab = 30, what is a² + b²?
29. 29.Use a² − b² = (a + b)(a − b) to find 48² − 11².
30. 30.Use (a − b)² = a² − 2ab + b² to find 72².
31. 31.Find the value of x² − y² when x = 6 and y = 4.
32. 32.Use (a + b)² = a² + 2ab + b² to find 97².
33. 33.Use (a + b)(a − b) = a² − b² to find 32 × 28.
34. 34.Find the value of x² + 2xy + y² when x = 9 and y = 5.
35. 35.Use (a + b)(a − b) = a² − b² to find 31 × 29.
36. 36.If a − b = 5 and ab = 6, what is a² + b²?
37. 37.Use (a + b)(a − b) = a² − b² to find 23 × 17.
38. 38.Find the value of x² − y² when x = 7 and y = 3.
39. 39.Use (a + b)² = a² + 2ab + b² to find 28².
40. 40.Use (a + b)² = a² + 2ab + b² to find 69².

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