Ontbinden in factoren (2)

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Zonder de gemeenschappelijke factor af. Ontbind verder in factoren indien mogelijk.

1. \(-36y^{7}+25y^{3}\)
2. \(24b^{15}-54b^{3}\)
3. \(75b^{15}-60b^{10}y+12b^{5}y^2\)
4. \(-384p^{8}-96p^{5}s-6p^{2}s^2\)
5. \(24y^{19}-6y^{5}\)
6. \(-54s^{8}-144s^{5}x-96s^{2}x^2\)
7. \(384a^{13}-672a^{8}+294a^{3}\)
8. \(-50p^{6}-40p^{4}-8p^{2}\)
9. \(180p^{9}+60p^{6}q+5p^{3}q^2\)
10. \(-80p^{4}+125p^{2}\)
11. \(150s^{5}-216s^{3}\)
12. \(216b^{9}+72b^{7}p+6b^{5}p^2\)

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Zonder de gemeenschappelijke factor af. Ontbind verder in factoren indien mogelijk.

Verbetersleutel

1. \(-36y^{7}+25y^{3}=-y^{3}(36y^{4}-25)=-y^{3}(6y^2+5)(6y^2-5)\)
2. \(24b^{15}-54b^{3}=6b^{3}(4b^{12}-9)=6b^{3}(2b^6+3)(2b^6-3)\)
3. \(75b^{15}-60b^{10}y+12b^{5}y^2=3b^{5}(25b^{10}-20b^5y+4y^2)=3b^{5}(5b^5-2y)^2\)
4. \(-384p^{8}-96p^{5}s-6p^{2}s^2=-6p^{2}(64p^{6}+16p^3s+s^2)=-6p^{2}(8p^3+s)^2\)
5. \(24y^{19}-6y^{5}=6y^{5}(4y^{14}-1)=6y^{5}(2y^7+1)(2y^7-1)\)
6. \(-54s^{8}-144s^{5}x-96s^{2}x^2=-6s^{2}(9s^{6}+24s^3x+16x^2)=-6s^{2}(3s^3+4x)^2\)
7. \(384a^{13}-672a^{8}+294a^{3}=6a^{3}(64a^{10}-112a^5+49)=6a^{3}(8a^5-7)^2\)
8. \(-50p^{6}-40p^{4}-8p^{2}=-2p^{2}(25p^{4}+20p^2+4)=-2p^{2}(5p^2+2)^2\)
9. \(180p^{9}+60p^{6}q+5p^{3}q^2=5p^{3}(36p^{6}+12p^3q+q^2)=5p^{3}(6p^3+q)^2\)
10. \(-80p^{4}+125p^{2}=-5p^{2}(16p^{2}-25)=-5p^{2}(4p+5)(4p-5)\)
11. \(150s^{5}-216s^{3}=6s^{3}(25s^{2}-36)=6s^{3}(5s+6)(5s-6)\)
12. \(216b^{9}+72b^{7}p+6b^{5}p^2=6b^{5}(36b^{4}+12b^2p+p^2)=6b^{5}(6b^2+p)^2\)