Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 200 · 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 a² − b² = (a + b)(a − b) to find 90² − 33².
2. 2.Use (a + b)(a − b) = a² − b² to find 45 × 35.
3. 3.Use (a + b)(a − b) = a² − b² to find 21 × 19.
4. 4.Use a² − b² = (a + b)(a − b) to find 23² − 21².
5. 5.Use a² − b² = (a + b)(a − b) to find 85² − 44².
6. 6.Use (a + b)(a − b) = a² − b² to find 34 × 26.
7. 7.Use (a − b)² = a² − 2ab + b² to find 31².
8. 8.Use (a + b)² = a² + 2ab + b² to find 39².
9. 9.Use (a + b)² = a² + 2ab + b² to find 82².
10. 10.Use (a + b)² = a² + 2ab + b² to find 71².
11. 11.Use (a + b)² = a² + 2ab + b² to find 31².
12. 12.If a − b = 7 and ab = 8, what is a² + b²?
13. 13.Use a² − b² = (a + b)(a − b) to find 69² − 59².
14. 14.Use (a + b)² = a² + 2ab + b² to find 56².
15. 15.Use (a + b)² = a² + 2ab + b² to find 61².
16. 16.If a + b = 7 and ab = 6, what is a² + b²?
17. 17.Use (a + b)(a − b) = a² − b² to find 96 × 84.
18. 18.Use (a + b)² = a² + 2ab + b² to find 11².
19. 19.If a + b = 10 and ab = 24, what is a² + b²?
20. 20.Use a² − b² = (a + b)(a − b) to find 55² − 10².
21. 21.Use (a − b)² = a² − 2ab + b² to find 95².
22. 22.Use (a + b)² = a² + 2ab + b² to find 48².
23. 23.If a + b = 13 and ab = 42, what is a² + b²?
24. 24.Find the value of x² + 2xy + y² when x = 4 and y = 3.
25. 25.Use (a − b)² = a² − 2ab + b² to find 63².
26. 26.Use a² − b² = (a + b)(a − b) to find 96² − 14².
27. 27.Find the value of x² + 2xy + y² when x = 6 and y = 1.
28. 28.Use (a − b)² = a² − 2ab + b² to find 48².
29. 29.If a + b = 3 and ab = 2, what is a² + b²?
30. 30.Use a² − b² = (a + b)(a − b) to find 96² − 37².
31. 31.Use (a + b)² = a² + 2ab + b² to find 14².
32. 32.Use (a + b)(a − b) = a² − b² to find 86 × 74.
33. 33.Find the value of x² − y² when x = 7 and y = 1.
34. 34.Use (a + b)² = a² + 2ab + b² to find 99².
35. 35.Use (a − b)² = a² − 2ab + b² to find 84².
36. 36.Use (a + b)(a − b) = a² − b² to find 106 × 94.
37. 37.Use (a + b)(a − b) = a² − b² to find 104 × 96.
38. 38.Use a² − b² = (a + b)(a − b) to find 59² − 32².
39. 39.If a + b = 15 and ab = 36, what is a² + b²?
40. 40.Use (a + b)² = a² + 2ab + b² to find 24².

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