Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 438 · 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 34 × 26.
2. 2.Use (a + b)(a − b) = a² − b² to find 103 × 97.
3. 3.Use a² − b² = (a + b)(a − b) to find 48² − 2².
4. 4.Use (a − b)² = a² − 2ab + b² to find 34².
5. 5.Use (a − b)² = a² − 2ab + b² to find 47².
6. 6.Use (a − b)² = a² − 2ab + b² to find 29².
7. 7.Use (a − b)² = a² − 2ab + b² to find 59².
8. 8.Find the value of x² + 2xy + y² when x = 10 and y = 1.
9. 9.Use (a + b)(a − b) = a² − b² to find 86 × 74.
10. 10.Use a² − b² = (a + b)(a − b) to find 73² − 46².
11. 11.Find the value of x² − y² when x = 14 and y = 10.
12. 12.Use (a + b)² = a² + 2ab + b² to find 101².
13. 13.If a − b = 4 and ab = 21, what is a² + b²?
14. 14.Find the value of x² − 2xy + y² when x = 3 and y = 2.
15. 15.Use (a + b)(a − b) = a² − b² to find 49 × 31.
16. 16.Find the value of x² − y² when x = 14 and y = 2.
17. 17.If a + b = 3 and ab = 2, what is a² + b²?
18. 18.If a − b = 1 and ab = 90, what is a² + b²?
19. 19.Use (a + b)² = a² + 2ab + b² to find 93².
20. 20.Use (a + b)² = a² + 2ab + b² to find 72².
21. 21.Use (a + b)² = a² + 2ab + b² to find 51².
22. 22.Use (a + b)² = a² + 2ab + b² to find 47².
23. 23.If a + b = 21 and ab = 110, what is a² + b²?
24. 24.Use a² − b² = (a + b)(a − b) to find 55² − 25².
25. 25.Use (a + b)(a − b) = a² − b² to find 31 × 29.
26. 26.Find the value of x² + 2xy + y² when x = 7 and y = 3.
27. 27.If a − b = 9 and ab = 10, what is a² + b²?
28. 28.Use (a + b)(a − b) = a² − b² to find 35 × 25.
29. 29.Use (a − b)² = a² − 2ab + b² to find 69².
30. 30.Use (a + b)(a − b) = a² − b² to find 104 × 96.
31. 31.If a + b = 9 and ab = 8, what is a² + b²?
32. 32.If a + b = 18 and ab = 80, what is a² + b²?
33. 33.Use (a + b)(a − b) = a² − b² to find 22 × 18.
34. 34.Use a² − b² = (a + b)(a − b) to find 64² − 19².
35. 35.Use (a + b)(a − b) = a² − b² to find 36 × 24.
36. 36.Use (a − b)² = a² − 2ab + b² to find 79².
37. 37.Use (a − b)² = a² − 2ab + b² to find 77².
38. 38.If a − b = 2 and ab = 24, what is a² + b²?
39. 39.Use (a + b)(a − b) = a² − b² to find 59 × 41.
40. 40.Use a² − b² = (a + b)(a − b) to find 72² − 59².

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