Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 528 · 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.Find the value of x² − y² when x = 12 and y = 4.
2. 2.Use (a + b)(a − b) = a² − b² to find 72 × 68.
3. 3.Use (a − b)² = a² − 2ab + b² to find 91².
4. 4.Use a² − b² = (a + b)(a − b) to find 49² − 10².
5. 5.Use (a + b)² = a² + 2ab + b² to find 54².
6. 6.Use a² − b² = (a + b)(a − b) to find 60² − 29².
7. 7.Use (a + b)(a − b) = a² − b² to find 107 × 93.
8. 8.Use (a + b)² = a² + 2ab + b² to find 25².
9. 9.Find the value of x² + 2xy + y² when x = 8 and y = 4.
10. 10.Find the value of x² − 2xy + y² when x = 4 and y = 3.
11. 11.Use (a − b)² = a² − 2ab + b² to find 85².
12. 12.Use (a − b)² = a² − 2ab + b² to find 89².
13. 13.Find the value of x² + 2xy + y² when x = 3 and y = 2.
14. 14.Use (a − b)² = a² − 2ab + b² to find 79².
15. 15.If a + b = 10 and ab = 21, what is a² + b²?
16. 16.Use (a + b)(a − b) = a² − b² to find 52 × 48.
17. 17.If a + b = 9 and ab = 18, what is a² + b²?
18. 18.Find the value of x² + 2xy + y² when x = 8 and y = 7.
19. 19.Use (a + b)² = a² + 2ab + b² to find 29².
20. 20.Use (a + b)² = a² + 2ab + b² to find 56².
21. 21.Find the value of x² + 2xy + y² when x = 15 and y = 5.
22. 22.Use (a + b)(a − b) = a² − b² to find 21 × 19.
23. 23.Use a² − b² = (a + b)(a − b) to find 55² − 44².
24. 24.If a + b = 9 and ab = 20, what is a² + b²?
25. 25.Use (a + b)(a − b) = a² − b² to find 97 × 83.
26. 26.Use a² − b² = (a + b)(a − b) to find 31² − 4².
27. 27.Use a² − b² = (a + b)(a − b) to find 21² − 1².
28. 28.Use (a + b)² = a² + 2ab + b² to find 48².
29. 29.Use (a + b)² = a² + 2ab + b² to find 85².
30. 30.Use (a + b)(a − b) = a² − b² to find 85 × 75.
31. 31.Use (a − b)² = a² − 2ab + b² to find 99².
32. 32.Use (a + b)(a − b) = a² − b² to find 63 × 57.
33. 33.Use (a + b)(a − b) = a² − b² to find 93 × 87.
34. 34.Find the value of x² + 2xy + y² when x = 14 and y = 5.
35. 35.Find the value of x² − y² when x = 4 and y = 3.
36. 36.Use (a − b)² = a² − 2ab + b² to find 59².
37. 37.Use (a + b)² = a² + 2ab + b² to find 84².
38. 38.Find the value of x² − y² when x = 5 and y = 3.
39. 39.If a − b = 9 and ab = 22, what is a² + b²?
40. 40.Use a² − b² = (a + b)(a − b) to find 31² − 23².

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