Ontbinden in factoren (2)

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

1. \(-5b^{5}-90b^{4}-405b^{3}\)
2. \(6p^{5}-6p^{3}\)
3. \(-5a^{5}+20a^{3}\)
4. \(150x^{9}-240x^{7}+96x^{5}\)
5. \(36s^{20}-s^{4}\)
6. \(-16b^{17}+b^{5}\)
7. \(-16y^{5}+49y^{3}\)
8. \(27y^{5}-48y^{3}\)
9. \(18b^{6}+48b^{4}+32b^{2}\)
10. \(-18s^{8}-12s^{6}x-2s^{4}x^2\)
11. \(5a^{6}-45a^{4}\)
12. \(9p^{9}-12p^{7}+4p^{5}\)

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

Verbetersleutel

1. \(-5b^{5}-90b^{4}-405b^{3}=-5b^{3}(b^2+18b+81)=-5b^{3}(b+9)^2\)
2. \(6p^{5}-6p^{3}=6p^{3}(p^2-1)=6p^{3}(p+1)(p-1)\)
3. \(-5a^{5}+20a^{3}=-5a^{3}(a^2-4)=-5a^{3}(a+2)(a-2)\)
4. \(150x^{9}-240x^{7}+96x^{5}=6x^{5}(25x^{4}-40x^2+16)=6x^{5}(5x^2-4)^2\)
5. \(36s^{20}-s^{4}=s^{4}(36s^{16}-1)=s^{4}(6s^8+1)(6s^8-1)\)
6. \(-16b^{17}+b^{5}=-b^{5}(16b^{12}-1)=-b^{5}(4b^6+1)(4b^6-1)\)
7. \(-16y^{5}+49y^{3}=-y^{3}(16y^{2}-49)=-y^{3}(4y+7)(4y-7)\)
8. \(27y^{5}-48y^{3}=3y^{3}(9y^{2}-16)=3y^{3}(3y+4)(3y-4)\)
9. \(18b^{6}+48b^{4}+32b^{2}=2b^{2}(9b^{4}+24b^2+16)=2b^{2}(3b^2+4)^2\)
10. \(-18s^{8}-12s^{6}x-2s^{4}x^2=-2s^{4}(9s^{4}+6s^2x+x^2)=-2s^{4}(3s^2+x)^2\)
11. \(5a^{6}-45a^{4}=5a^{4}(a^2-9)=5a^{4}(a+3)(a-3)\)
12. \(9p^{9}-12p^{7}+4p^{5}=p^{5}(9p^{4}-12p^2+4)=p^{5}(3p^2-2)^2\)