Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 150 · 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 78 × 62.
2. 2.Use a² − b² = (a + b)(a − b) to find 44² − 7².
3. 3.Use (a + b)² = a² + 2ab + b² to find 12².
4. 4.Find the value of x² − y² when x = 8 and y = 4.
5. 5.Use (a + b)² = a² + 2ab + b² to find 88².
6. 6.Use a² − b² = (a + b)(a − b) to find 30² − 3².
7. 7.Use (a + b)(a − b) = a² − b² to find 73 × 67.
8. 8.Use (a − b)² = a² − 2ab + b² to find 45².
9. 9.If a − b = 1 and ab = 72, what is a² + b²?
10. 10.Use a² − b² = (a + b)(a − b) to find 77² − 21².
11. 11.Use (a + b)(a − b) = a² − b² to find 23 × 17.
12. 12.Use a² − b² = (a + b)(a − b) to find 55² − 2².
13. 13.Use (a + b)(a − b) = a² − b² to find 65 × 55.
14. 14.If a + b = 14 and ab = 48, what is a² + b²?
15. 15.If a + b = 7 and ab = 12, what is a² + b²?
16. 16.If a − b = 10 and ab = 24, what is a² + b²?
17. 17.Use a² − b² = (a + b)(a − b) to find 93² − 18².
18. 18.Use a² − b² = (a + b)(a − b) to find 68² − 8².
19. 19.Use a² − b² = (a + b)(a − b) to find 98² − 7².
20. 20.Use (a + b)(a − b) = a² − b² to find 93 × 87.
21. 21.Use (a + b)(a − b) = a² − b² to find 102 × 98.
22. 22.If a − b = 6 and ab = 16, what is a² + b²?
23. 23.Use (a − b)² = a² − 2ab + b² to find 33².
24. 24.Find the value of x² − 2xy + y² when x = 4 and y = 1.
25. 25.Find the value of x² + 2xy + y² when x = 14 and y = 3.
26. 26.Use a² − b² = (a + b)(a − b) to find 98² − 61².
27. 27.Use a² − b² = (a + b)(a − b) to find 94² − 88².
28. 28.Use (a − b)² = a² − 2ab + b² to find 13².
29. 29.Use a² − b² = (a + b)(a − b) to find 72² − 37².
30. 30.Use (a − b)² = a² − 2ab + b² to find 85².
31. 31.If a − b = 1 and ab = 12, what is a² + b²?
32. 32.Use (a + b)(a − b) = a² − b² to find 105 × 95.
33. 33.If a + b = 4 and ab = 3, what is a² + b²?
34. 34.Use (a + b)² = a² + 2ab + b² to find 79².
35. 35.Find the value of x² − 2xy + y² when x = 3 and y = 1.
36. 36.Use (a + b)² = a² + 2ab + b² to find 15².
37. 37.Find the value of x² + 2xy + y² when x = 9 and y = 4.
38. 38.Use a² − b² = (a + b)(a − b) to find 89² − 65².
39. 39.Use (a + b)² = a² + 2ab + b² to find 23².
40. 40.Use (a + b)² = a² + 2ab + b² to find 21².

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