imath - Graad 10 oefeninge i.v.m. die produk van tweeterm met drieterm om som of verskil van derde magte te vorm

WISKUNDE
Graad 10
NOG OEFENINGE
Produk is die som of verskil van twee derdemagte.

Vraag 1

Bepaal die volgende produkte :

$$ \hspace*{6 mm}\mathrm{1.\kern2mm\ (a + b)(a^2 - ab + b^2) } $$

[ Antwoord 1. ]

$$ \hspace*{6 mm}\mathrm{2.\kern2mm\ (a - b)(a^2 + ab + b^2) } $$

[ Antwoord 2. ]

$$ \hspace*{6 mm}\mathrm{3.\kern2mm\ (c + d)(c^2 - cd + d^2) } $$

[ A 3. ]

$$ \hspace*{6 mm}\mathrm{4.\kern2mm\ (m - n)(m^2 + mn + n^2) } $$

[ A 4. ]

$$ \hspace*{6 mm}\mathrm{5.\kern2mm\ (p - q)(p^2 + pq + q^2) } $$

[ A 5. ]

$$ \hspace*{6 mm}\mathrm{6.\kern2mm\ (x + y)(x^2 - xy + y^2) } $$

[ A 6. ]

$$ \hspace*{6 mm}\mathrm{7.\kern2mm\ (a + 1)(a^2 - a + 1) } $$

[ A 7. ]

$$ \hspace*{6 mm}\mathrm{8.\kern2mm\ (b - 2)(b^2 + 2b + 4) } $$

[ A 8. ]

$$ \hspace*{6 mm}\mathrm{9.\kern2mm\ (c + 3)(c^2 - 3c + 9) } $$

[ A 9. ]

$$ \hspace*{6 mm}\mathrm{10.\kern2mm\ (f - 4)(f^2 + 4f + 16) } $$

[ A 10. ]

$$ \hspace*{6 mm}\mathrm{11.\kern2mm\ (m - 5)(m^2 + 5m + 25) } $$

[ A 11. ]

$$ \hspace*{6 mm}\mathrm{12.\kern2mm\ (n + 9)(n^2 - 9n + 81) } $$

[ A 12. ]

$$ \hspace*{6 mm}\mathrm{13.\kern2mm\ (x − \frac{1}{2})(x^2 + \frac{1}{2} x + \frac{1}{4}) } $$

[ A 13. ]

$$ \hspace*{6 mm}\mathrm{14.\kern2mm\ (y − \frac{1}{3})(y^2 + \frac{1}{3} y + \frac{1}{9}) } $$

[ A 14. ]

$$ \hspace*{6 mm}\mathrm{15.\kern2mm\ (a − \frac{2}{3})(a^2 + \frac{2}{3} a + \frac{4}{9}) } $$

[ A 15. ]

$$ \hspace*{6 mm}\mathrm{16.\kern2mm\ (b − \frac{1}{5})(b² + \frac{b}{5} + \frac{1}{25}) } $$

[ A 16. ]

$$ \hspace*{6 mm}\mathrm{17.\kern2mm\ (d + \frac{3}{2})(d² − \frac{3d}{2} + \frac{9}{4}) } $$

[ A 17. ]

$$ \hspace*{6 mm}\mathrm{18.\kern2mm\ (c + \frac{2}{3})(c² − \frac{2c}{3} + \frac{4}{9}) } $$

[ A 18. ]

$$ \hspace*{6 mm}\mathrm{19.\kern2mm\ (m - 0,1)(m² + 0,1m + 0,01) } $$

[ A 19. ]

$$ \hspace*{6 mm}\mathrm{20.\kern2mm\ (n + 0,2)(n² - 0,2n + 0,04) } $$

[ A 20. ]

$$ \hspace*{6 mm}\mathrm{21.\kern2mm\ (n + 0,15)(n^2 - 0,15n + 0,0225) } $$

[ A 21. ]

$$ \hspace*{6 mm}\mathrm{22.\kern2mm\ (p + 0,6)(p^2 - 0,6p + 0,36) } $$

[ A 22. ]

$$ \hspace*{6 mm}\mathrm{23.\kern2mm\ (q - 0,3)(q^2 + 0,3q + 0,09) } $$

[ A 23. ]

$$ \hspace*{6 mm}\mathrm{24.\kern2mm\ (2p + 1)(4p^2 - 2p + 1) } $$

[ A 24. ]

$$ \hspace*{6 mm}\mathrm{25.\kern2mm\ (3q + 2)(9q^2 - 6q + 4) } $$

[ A 25. ]

$$ \hspace*{6 mm}\mathrm{26.\kern2mm\ (3a - 2)(9a^2 + 6a + 4) } $$

[ A 26. ]

$$ \hspace*{6 mm}\mathrm{27.\kern2mm\ (5b + 4)(25b^2 - 20b + 16) } $$

[ A 27. ]

$$ \hspace*{6 mm}\mathrm{28.\kern2mm\ (2p + q)(4p^2 - 2pq + q^2) } $$

[ A 28. ]

$$ \hspace*{6 mm}\mathrm{29.\kern2mm\ (3q + 2a)(9q^2 - 6aq + 4a^2) } $$

[ A 29. ]

$$ \hspace*{6 mm}\mathrm{30.\kern2mm\ (3a - 2b)(9a^2 + 6ab + 4b^2) } $$

[ A 30. ]

$$ \hspace*{6 mm}\mathrm{31.\kern2mm\ (5b + 4m)(25b^2 - 20bm + 16m*2) } $$

[ A 31. ]

$$ \hspace*{6 mm}\mathrm{32.\kern2mm\ (1 + a)(1 - a + a^2) } $$

[ A 32. ]

$$ \hspace*{6 mm}\mathrm{33.\kern2mm\ (3 + b)(9 - 3b + b^2) } $$

[ A 33. ]

$$ \hspace*{6 mm}\mathrm{34.\kern2mm\ (5 - c)(25 + 5c + c^2) } $$

[ A 34. ]

$$ \hspace*{6 mm}\mathrm{35.\kern2mm\ (b + 4m)(b^2 - 4bm + 16m^2) } $$

[ A 35. ]

$$ \hspace*{6 mm}\mathrm{36.\kern2mm\ (p + a)(p^2 - ap + a^2) } $$

[ A 36. ]

$$ \hspace*{6 mm}\mathrm{37.\kern2mm\ (3a + b)(9a^2 - 3ab + b^2) } $$

[ A 37. ]

$$ \hspace*{6 mm}\mathrm{38.\kern2mm\ (5b - 2c)(25b^2 + 10bc + 4c^2) } $$

[ A 38. ]

$$ \hspace*{6 mm}\mathrm{39.\kern2mm\ (3p + 4q)(9p^2 - 12pq + 16q^2) } $$

[ A 39. ]

$$ \hspace*{6 mm}\mathrm{40.\kern2mm\ (5x - 7y)(25x^2 + 35xy + 49y^2) } $$

[ A 40. ]

Vraag 1
Bepaal die volgende produkte :

$$ \hspace*{6 mm}\mathrm{1.\kern2mm\ (a + b)(a^2 - ab + b^2) } $$