Ontbinden in factoren (2)

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

1. \(-3b^{7}-24b^{6}-48b^{5}\)
2. \(-p^{6}-14p^{5}-49p^{4}\)
3. \(180y^{6}-245y^{4}\)
4. \(-6b^{4}+96b^{2}\)
5. \(-48b^{20}+27b^{4}\)
6. \(245s^{13}+140s^{9}y+20s^{5}y^2\)
7. \(16y^{15}+40y^{10}+25y^{5}\)
8. \(75s^{7}+90s^{6}+27s^{5}\)
9. \(-216a^{13}-360a^{8}p-150a^{3}p^2\)
10. \(3y^{4}-27y^{2}\)
11. \(45a^{7}-20a^{5}\)
12. \(180p^{7}-125p^{5}\)

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

Verbetersleutel

1. \(-3b^{7}-24b^{6}-48b^{5}=-3b^{5}(b^2+8b+16)=-3b^{5}(b+4)^2\)
2. \(-p^{6}-14p^{5}-49p^{4}=-p^{4}(p^2+14p+49)=-p^{4}(p+7)^2\)
3. \(180y^{6}-245y^{4}=5y^{4}(36y^{2}-49)=5y^{4}(6y+7)(6y-7)\)
4. \(-6b^{4}+96b^{2}=-6b^{2}(b^2-16)=-6b^{2}(b-4)(b+4)\)
5. \(-48b^{20}+27b^{4}=-3b^{4}(16b^{16}-9)=-3b^{4}(4b^8+3)(4b^8-3)\)
6. \(245s^{13}+140s^{9}y+20s^{5}y^2=5s^{5}(49s^{8}+28s^4y+4y^2)=5s^{5}(7s^4+2y)^2\)
7. \(16y^{15}+40y^{10}+25y^{5}=y^{5}(16y^{10}+40y^5+25)=y^{5}(4y^5+5)^2\)
8. \(75s^{7}+90s^{6}+27s^{5}=3s^{5}(25s^{2}+30s+9)=3s^{5}(5s+3)^2\)
9. \(-216a^{13}-360a^{8}p-150a^{3}p^2=-6a^{3}(36a^{10}+60a^5p+25p^2)=-6a^{3}(6a^5+5p)^2\)
10. \(3y^{4}-27y^{2}=3y^{2}(y^2-9)=3y^{2}(y-3)(y+3)\)
11. \(45a^{7}-20a^{5}=5a^{5}(9a^{2}-4)=5a^{5}(3a+2)(3a-2)\)
12. \(180p^{7}-125p^{5}=5p^{5}(36p^{2}-25)=5p^{5}(6p+5)(6p-5)\)