Ontbinden in factoren (2)

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

1. \(-216p^{13}+360p^{9}y-150p^{5}y^2\)
2. \(50a^{9}-72a^{5}\)
3. \(-8b^{9}-8b^{7}-2b^{5}\)
4. \(-180q^{9}-300q^{7}x-125q^{5}x^2\)
5. \(108s^{7}-3s^{5}\)
6. \(5s^{5}-320s^{3}\)
7. \(-45p^{12}-120p^{7}y-80p^{2}y^2\)
8. \(-80x^{5}-200x^{4}-125x^{3}\)
9. \(2a^{5}-12a^{4}+18a^{3}\)
10. \(8b^{14}+8b^{9}+2b^{4}\)
11. \(8x^{5}-98x^{3}\)
12. \(-48s^{5}+147s^{3}\)

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

Verbetersleutel

1. \(-216p^{13}+360p^{9}y-150p^{5}y^2=-6p^{5}(36p^{8}-60p^4y+25y^2)=-6p^{5}(6p^4-5y)^2\)
2. \(50a^{9}-72a^{5}=2a^{5}(25a^{4}-36)=2a^{5}(5a^2+6)(5a^2-6)\)
3. \(-8b^{9}-8b^{7}-2b^{5}=-2b^{5}(4b^{4}+4b^2+1)=-2b^{5}(2b^2+1)^2\)
4. \(-180q^{9}-300q^{7}x-125q^{5}x^2=-5q^{5}(36q^{4}+60q^2x+25x^2)=-5q^{5}(6q^2+5x)^2\)
5. \(108s^{7}-3s^{5}=3s^{5}(36s^{2}-1)=3s^{5}(6s+1)(6s-1)\)
6. \(5s^{5}-320s^{3}=5s^{3}(s^2-64)=5s^{3}(s-8)(s+8)\)
7. \(-45p^{12}-120p^{7}y-80p^{2}y^2=-5p^{2}(9p^{10}+24p^5y+16y^2)=-5p^{2}(3p^5+4y)^2\)
8. \(-80x^{5}-200x^{4}-125x^{3}=-5x^{3}(16x^{2}+40x+25)=-5x^{3}(4x+5)^2\)
9. \(2a^{5}-12a^{4}+18a^{3}=2a^{3}(a^2-6a+9)=2a^{3}(a-3)^2\)
10. \(8b^{14}+8b^{9}+2b^{4}=2b^{4}(4b^{10}+4b^5+1)=2b^{4}(2b^5+1)^2\)
11. \(8x^{5}-98x^{3}=2x^{3}(4x^{2}-49)=2x^{3}(2x+7)(2x-7)\)
12. \(-48s^{5}+147s^{3}=-3s^{3}(16s^{2}-49)=-3s^{3}(4s+7)(4s-7)\)