MATHEMATICS
Grade 10
MORE EXERCISES
Factors of the difference between two squares.
Question 1
Factorize fully :
$$ \hspace*{6 mm}\mathrm{1.\kern2mm\ a^2 − b^2 } $$
[ Answer 1. ]
$$ \hspace*{6 mm}\mathrm{2.\kern2mm\ c^2 - d^2 } $$
[ Answer 2. ]
$$ \hspace*{6 mm}\mathrm{3.\kern2mm\ m^2 - n^2 } $$
[ A 3. ]
$$ \hspace*{6 mm}\mathrm{4.\kern2mm\ p^2 - q^2 } $$
[ A 4. ]
$$ \hspace*{6 mm}\mathrm{5.\kern2mm\ x^2 - y^2 } $$
[ A 5. ]
$$ \hspace*{6 mm}\mathrm{6.\kern2mm\ a^2 - 4 } $$
[ A 6. ]
$$ \hspace*{6 mm}\mathrm{7.\kern2mm\ b^2 - 16 } $$
[ A 7. ]
$$ \hspace*{6 mm}\mathrm{8.\kern2mm\ c^2 - 36 } $$
[ A 8. ]
$$ \hspace*{6 mm}\mathrm{9.\kern2mm\ d^2 - 100 } $$
[ A 9. ]
$$ \hspace*{6 mm}\mathrm{10.\kern2mm\ h^2 - 225 } $$
[ A 10. ]
$$ \hspace*{6 mm}\mathrm{11.\kern2mm\ m^2 - 144 } $$
[ A 11. ]
$$ \hspace*{6 mm}\mathrm{12.\kern2mm\ n^2 - 289 } $$
[ A 12. ]
$$ \hspace*{6 mm}\mathrm{13.\kern2mm\ p^2 - \frac{1}{4} } $$
[ A 13. ]
$$ \hspace*{6 mm}\mathrm{14.\kern2mm\ q^2 - \frac{1}{25} } $$
[ A 14. ]
$$ \hspace*{6 mm}\mathrm{15.\kern2mm\ x^2 - \frac{1}{36} } $$
[ A 15. ]
$$ \hspace*{6 mm}\mathrm{16.\kern2mm\ y^2 - \frac{16}{25} } $$
[ A 16. ]
$$ \hspace*{6 mm}\mathrm{17.\kern2mm\ z^2 - \frac{49}{36} } $$
[ A 17. ]
$$ \hspace*{6 mm}\mathrm{18.\kern2mm\ a^2 - \frac{4b^2}{81} } $$
[ A 18. ]
$$ \hspace*{6 mm}\mathrm{19.\kern2mm\ x^2 - 0,01 } $$
[ A 19. ]
$$ \hspace*{6 mm}\mathrm{20.\kern2mm\ y^2 - 0,09 } $$
[ A 20. ]
$$ \hspace*{6 mm}\mathrm{21.\kern2mm\ z^2 - 0,0256 } $$
[ A 21. ]
$$ \hspace*{6 mm}\mathrm{22.\kern2mm\ a^2 - 0,16 } $$
[ A 22. ]
$$ \hspace*{6 mm}\mathrm{23.\kern2mm\ 9b^2 - 16 } $$
[ A 23. ]
$$ \hspace*{6 mm}\mathrm{24.\kern2mm\ 25c^2 - 49 } $$
[ A 24. ]
$$ \hspace*{6 mm}\mathrm{25.\kern2mm\ 16m^2 - 49n^2 } $$
[ A 25. ]
$$ \hspace*{6 mm}\mathrm{26.\kern2mm\ 25n^2 - 81p^2 } $$
[ A 26. ]
$$ \hspace*{6 mm}\mathrm{27.\kern2mm\ 121p^2q^2 - 225x^2y^2 } $$
[ A 27. ]
$$ \hspace*{6 mm}\mathrm{28.\kern2mm\ \frac{a^2}{16} − \frac{25}{ b^2} } $$
[ A 28. ]
$$ \hspace*{6 mm}\mathrm{29.\kern2mm\ \frac{9c^2}{16d^2} − \frac{25}{81} } $$
[ A 29. ]
$$ \hspace*{6 mm}\mathrm{30.\kern2mm\ \frac{16x^2}{49y^2} − \frac{81p^2}{121q^2} } $$
[ A 30. ]
$$ \hspace*{6 mm}\mathrm{31.\kern2mm\ \frac{121a^2}{144b^2} − \frac{169c^2}{225d^2} } $$
[ A 31. ]
$$ \hspace*{6 mm}\mathrm{32.\kern2mm\ \frac{4a^2b^2}{9p^2} − \frac{25c^2d^2}{16q^2} } $$
[ A 32. ]
$$ \hspace*{6 mm}\mathrm{33.\kern2mm\ 4a^2 − 3b^2 } $$
[ A 33. ]
$$ \hspace*{6 mm}\mathrm{34.\kern2mm\ 5p^2 − 13q^2 } $$
[ A 34. ]
$$ \hspace*{6 mm}\mathrm{35.\kern2mm\ 3a^2 − 5b^2 } $$
[ A 35. ]
$$ \hspace*{6 mm}\mathrm{36.\kern2mm\ p^2 − \frac{q^2}{3} } $$
[ A 36. ]
$$ \hspace*{6 mm}\mathrm{37.\kern2mm\ p^2 − \frac{2q^2}{3} } $$
[ A 37. ]
$$ \hspace*{6 mm}\mathrm{38.\kern2mm\ \frac{3a^2}{5b^2} − \frac{7p^2}{17q^2} } $$
[ A 38. ]
$$ \hspace*{6 mm}\mathrm{39.\kern2mm\ a^4 − b^4 } $$
[ A 39. ]
$$ \hspace*{6 mm}\mathrm{40.\kern2mm\ p^4 − q^4 } $$
[ A 40. ]
$$ \hspace*{6 mm}\mathrm{41.\kern2mm\ p^6 − q^6 } $$
[ A 41. ]
$$ \hspace*{6 mm}\mathrm{42.\kern2mm\ x^8 − y^8 } $$
[ A 42. ]
$$ \hspace*{6 mm}\mathrm{43.\kern2mm\ x^{10} − \frac{1}{4} } $$
[ A 43. ]
$$ \hspace*{6 mm}\mathrm{44.\kern2mm\ x^8 − \frac{16}{81} } $$
[ A 44. ]
Question 1
Factorize fully :
$$ \hspace*{6 mm}\mathrm{1.\kern2mm\ a^2 − b^2 } $$
[ Answer 1. ]
$$ \hspace*{6 mm}\mathrm{3.\kern2mm\ m^2 - n^2 } $$
[ A 3. ]
$$ \hspace*{6 mm}\mathrm{5.\kern2mm\ x^2 - y^2 } $$
[ A 5. ]
$$ \hspace*{6 mm}\mathrm{7.\kern2mm\ b^2 - 16 } $$
[ A 7. ]
$$ \hspace*{6 mm}\mathrm{9.\kern2mm\ d^2 - 100 } $$
[ A 9. ]
$$ \hspace*{6 mm}\mathrm{11.\kern2mm\ m^2 - 144 } $$
[ A 11. ]
$$ \hspace*{6 mm}\mathrm{13.\kern2mm\ p^2 - \frac{1}{4} } $$
[ A 13. ]
$$ \hspace*{6 mm}\mathrm{15.\kern2mm\ x^2 - \frac{1}{36} } $$
[ A 15. ]
$$ \hspace*{6 mm}\mathrm{17.\kern2mm\ z^2 - \frac{49}{36} } $$
[ A 17. ]
$$ \hspace*{6 mm}\mathrm{19.\kern2mm\ x^2 - 0,01 } $$
[ A 19. ]
$$ \hspace*{6 mm}\mathrm{21.\kern2mm\ z^2 - 0,0256 } $$
[ A 21. ]
$$ \hspace*{6 mm}\mathrm{23.\kern2mm\ 9b^2 - 16 } $$
[ A 23. ]
$$ \hspace*{6 mm}\mathrm{25.\kern2mm\ 16m^2 - 49n^2 } $$
[ A 25. ]
$$ \hspace*{6 mm}\mathrm{27.\kern2mm\ 121p^2q^2 - 225x^2y^2 } $$
[ A 27. ]
$$ \hspace*{6 mm}\mathrm{29.\kern2mm\ \frac{9c^2}{16d^2} − \frac{25}{81} } $$
[ A 29. ]
$$ \hspace*{6 mm}\mathrm{31.\kern2mm\ \frac{121a^2}{144b^2} − \frac{169c^2}{225d^2} } $$
[ A 31. ]
$$ \hspace*{6 mm}\mathrm{33.\kern2mm\ 4a^2 − 3b^2 } $$
[ A 33. ]
$$ \hspace*{6 mm}\mathrm{35.\kern2mm\ 3a^2 − 5b^2 } $$
[ A 35. ]
$$ \hspace*{6 mm}\mathrm{37.\kern2mm\ p^2 − \frac{2q^2}{3} } $$
[ A 37. ]
$$ \hspace*{6 mm}\mathrm{39.\kern2mm\ a^4 − b^4 } $$
[ A 39. ]
$$ \hspace*{6 mm}\mathrm{41.\kern2mm\ p^6 − q^6 } $$
[ A 41. ]
$$ \hspace*{6 mm}\mathrm{43.\kern2mm\ x^{10} − \frac{1}{4} } $$
[ A 43. ]
$$ \hspace*{6 mm}\mathrm{2.\kern2mm\ c^2 - d^2 } $$
[ Answer 2. ]
$$ \hspace*{6 mm}\mathrm{4.\kern2mm\ p^2 - q^2 } $$
[ A 4. ]
$$ \hspace*{6 mm}\mathrm{6.\kern2mm\ a^2 - 4 } $$
[ A 6. ]
$$ \hspace*{6 mm}\mathrm{8.\kern2mm\ c^2 - 36 } $$
[ A 8. ]
$$ \hspace*{6 mm}\mathrm{10.\kern2mm\ h^2 - 225 } $$
[ A 10. ]
$$ \hspace*{6 mm}\mathrm{12.\kern2mm\ n^2 - 289 } $$
[ A 12. ]
$$ \hspace*{6 mm}\mathrm{14.\kern2mm\ q^2 - \frac{1}{25} } $$
[ A 14. ]
$$ \hspace*{6 mm}\mathrm{16.\kern2mm\ y^2 - \frac{16}{25} } $$
[ A 16. ]
$$ \hspace*{6 mm}\mathrm{18.\kern2mm\ a^2 - \frac{4b^2}{81} } $$
[ A 18. ]
$$ \hspace*{6 mm}\mathrm{20.\kern2mm\ y^2 - 0,09 } $$
[ A 20. ]
$$ \hspace*{6 mm}\mathrm{22.\kern2mm\ a^2 - 0,16 } $$
[ A 22. ]
$$ \hspace*{6 mm}\mathrm{24.\kern2mm\ 25c^2 - 49 } $$
[ A 24. ]
$$ \hspace*{6 mm}\mathrm{26.\kern2mm\ 25n^2 - 81p^2 } $$
[ A 26. ]
$$ \hspace*{6 mm}\mathrm{28.\kern2mm\ \frac{a^2}{16} − \frac{25}{ b^2} } $$
[ A 28. ]
$$ \hspace*{6 mm}\mathrm{30.\kern2mm\ \frac{16x^2}{49y^2} − \frac{81p^2}{121q^2} } $$
[ A 30. ]
$$ \hspace*{6 mm}\mathrm{32.\kern2mm\ \frac{4a^2b^2}{9p^2} − \frac{25c^2d^2}{16q^2} } $$
[ A 32. ]
$$ \hspace*{6 mm}\mathrm{34.\kern2mm\ 5p^2 − 13q^2 } $$
[ A 34. ]
$$ \hspace*{6 mm}\mathrm{36.\kern2mm\ p^2 − \frac{q^2}{3} } $$
[ A 36. ]
$$ \hspace*{6 mm}\mathrm{38.\kern2mm\ \frac{3a^2}{5b^2} − \frac{7p^2}{17q^2} } $$
[ A 38. ]
$$ \hspace*{6 mm}\mathrm{40.\kern2mm\ p^4 − q^4 } $$
[ A 40. ]
$$ \hspace*{6 mm}\mathrm{42.\kern2mm\ x^8 − y^8 } $$
[ A 42. ]
$$ \hspace*{6 mm}\mathrm{44.\kern2mm\ x^8 − \frac{16}{81} } $$
[ A 44. ]
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