Ontbinden in factoren (2)

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

1. \(-12s^{13}+75s^{5}\)
2. \(-108y^{12}+75y^{4}\)
3. \(-32s^{8}+48s^{5}x-18s^{2}x^2\)
4. \(32q^{9}-48q^{6}+18q^{3}\)
5. \(-20q^{15}+245q^{3}\)
6. \(96b^{11}-294b^{3}\)
7. \(27x^{11}-48x^{5}\)
8. \(-147p^{9}-42p^{7}q-3p^{5}q^2\)
9. \(3a^{4}-54a^{3}+243a^{2}\)
10. \(18a^{12}+48a^{7}p+32a^{2}p^2\)
11. \(294p^{8}+84p^{5}+6p^{2}\)
12. \(150a^{10}-240a^{7}+96a^{4}\)

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

Verbetersleutel

1. \(-12s^{13}+75s^{5}=-3s^{5}(4s^{8}-25)=-3s^{5}(2s^4+5)(2s^4-5)\)
2. \(-108y^{12}+75y^{4}=-3y^{4}(36y^{8}-25)=-3y^{4}(6y^4+5)(6y^4-5)\)
3. \(-32s^{8}+48s^{5}x-18s^{2}x^2=-2s^{2}(16s^{6}-24s^3x+9x^2)=-2s^{2}(4s^3-3x)^2\)
4. \(32q^{9}-48q^{6}+18q^{3}=2q^{3}(16q^{6}-24q^3+9)=2q^{3}(4q^3-3)^2\)
5. \(-20q^{15}+245q^{3}=-5q^{3}(4q^{12}-49)=-5q^{3}(2q^6+7)(2q^6-7)\)
6. \(96b^{11}-294b^{3}=6b^{3}(16b^{8}-49)=6b^{3}(4b^4+7)(4b^4-7)\)
7. \(27x^{11}-48x^{5}=3x^{5}(9x^{6}-16)=3x^{5}(3x^3+4)(3x^3-4)\)
8. \(-147p^{9}-42p^{7}q-3p^{5}q^2=-3p^{5}(49p^{4}+14p^2q+q^2)=-3p^{5}(7p^2+q)^2\)
9. \(3a^{4}-54a^{3}+243a^{2}=3a^{2}(a^2-18a+81)=3a^{2}(a-9)^2\)
10. \(18a^{12}+48a^{7}p+32a^{2}p^2=2a^{2}(9a^{10}+24a^5p+16p^2)=2a^{2}(3a^5+4p)^2\)
11. \(294p^{8}+84p^{5}+6p^{2}=6p^{2}(49p^{6}+14p^3+1)=6p^{2}(7p^3+1)^2\)
12. \(150a^{10}-240a^{7}+96a^{4}=6a^{4}(25a^{6}-40a^3+16)=6a^{4}(5a^3-4)^2\)