Ontbinden in factoren (2)

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

1. \(-48a^{6}+3a^{4}\)
2. \(-16s^{6}+49s^{4}\)
3. \(50p^{5}+20p^{4}+2p^{3}\)
4. \(-a^{6}+12a^{5}-36a^{4}\)
5. \(a^{6}-36a^{4}\)
6. \(-6q^{5}+60q^{4}-150q^{3}\)
7. \(-x^{4}-18x^{3}-81x^{2}\)
8. \(-27b^{6}+12b^{4}\)
9. \(-3p^{4}+3p^{2}\)
10. \(48b^{7}-27b^{5}\)
11. \(-6x^{6}+294x^{4}\)
12. \(32a^{15}-98a^{3}\)

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

Verbetersleutel

1. \(-48a^{6}+3a^{4}=-3a^{4}(16a^{2}-1)=-3a^{4}(4a+1)(4a-1)\)
2. \(-16s^{6}+49s^{4}=-s^{4}(16s^{2}-49)=-s^{4}(4s+7)(4s-7)\)
3. \(50p^{5}+20p^{4}+2p^{3}=2p^{3}(25p^{2}+10p+1)=2p^{3}(5p+1)^2\)
4. \(-a^{6}+12a^{5}-36a^{4}=-a^{4}(a^2-12a+36)=-a^{4}(a-6)^2\)
5. \(a^{6}-36a^{4}=a^{4}(a^2-36)=a^{4}(a-6)(a+6)\)
6. \(-6q^{5}+60q^{4}-150q^{3}=-6q^{3}(q^2-10q+25)=-6q^{3}(q-5)^2\)
7. \(-x^{4}-18x^{3}-81x^{2}=-x^{2}(x^2+18x+81)=-x^{2}(x+9)^2\)
8. \(-27b^{6}+12b^{4}=-3b^{4}(9b^{2}-4)=-3b^{4}(3b+2)(3b-2)\)
9. \(-3p^{4}+3p^{2}=-3p^{2}(p^2-1)=-3p^{2}(p-1)(p+1)\)
10. \(48b^{7}-27b^{5}=3b^{5}(16b^{2}-9)=3b^{5}(4b+3)(4b-3)\)
11. \(-6x^{6}+294x^{4}=-6x^{4}(x^2-49)=-6x^{4}(x+7)(x-7)\)
12. \(32a^{15}-98a^{3}=2a^{3}(16a^{12}-49)=2a^{3}(4a^6+7)(4a^6-7)\)