Ontbinden in factoren (2)

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

1. \(-3a^{4}+18a^{3}-27a^{2}\)
2. \(-16q^{5}+49q^{3}\)
3. \(50x^{6}-2x^{4}\)
4. \(-32s^{12}+50s^{4}\)
5. \(-6x^{7}+108x^{6}-486x^{5}\)
6. \(-24p^{13}-24p^{8}-6p^{3}\)
7. \(-12b^{6}-12b^{4}-3b^{2}\)
8. \(-5b^{7}+80b^{5}\)
9. \(20b^{8}+100b^{6}q+125b^{4}q^2\)
10. \(54x^{5}-294x^{3}\)
11. \(72p^{7}-50p^{5}\)
12. \(5b^{4}+80b^{3}+320b^{2}\)

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

Verbetersleutel

1. \(-3a^{4}+18a^{3}-27a^{2}=-3a^{2}(a^2-6a+9)=-3a^{2}(a-3)^2\)
2. \(-16q^{5}+49q^{3}=-q^{3}(16q^{2}-49)=-q^{3}(4q+7)(4q-7)\)
3. \(50x^{6}-2x^{4}=2x^{4}(25x^{2}-1)=2x^{4}(5x+1)(5x-1)\)
4. \(-32s^{12}+50s^{4}=-2s^{4}(16s^{8}-25)=-2s^{4}(4s^4+5)(4s^4-5)\)
5. \(-6x^{7}+108x^{6}-486x^{5}=-6x^{5}(x^2-18x+81)=-6x^{5}(x-9)^2\)
6. \(-24p^{13}-24p^{8}-6p^{3}=-6p^{3}(4p^{10}+4p^5+1)=-6p^{3}(2p^5+1)^2\)
7. \(-12b^{6}-12b^{4}-3b^{2}=-3b^{2}(4b^{4}+4b^2+1)=-3b^{2}(2b^2+1)^2\)
8. \(-5b^{7}+80b^{5}=-5b^{5}(b^2-16)=-5b^{5}(b+4)(b-4)\)
9. \(20b^{8}+100b^{6}q+125b^{4}q^2=5b^{4}(4b^{4}+20b^2q+25q^2)=5b^{4}(2b^2+5q)^2\)
10. \(54x^{5}-294x^{3}=6x^{3}(9x^{2}-49)=6x^{3}(3x+7)(3x-7)\)
11. \(72p^{7}-50p^{5}=2p^{5}(36p^{2}-25)=2p^{5}(6p+5)(6p-5)\)
12. \(5b^{4}+80b^{3}+320b^{2}=5b^{2}(b^2+16b+64)=5b^{2}(b+8)^2\)