Ontbinden in factoren (2)

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

1. \(6a^{6}-12a^{5}+6a^{4}\)
2. \(180p^{5}-5p^{3}\)
3. \(16a^{5}-56a^{4}+49a^{3}\)
4. \(5x^{4}-125x^{2}\)
5. \(-245a^{12}-420a^{8}-180a^{4}\)
6. \(-18p^{7}+24p^{6}-8p^{5}\)
7. \(4y^{9}-y^{5}\)
8. \(54x^{13}+36x^{8}+6x^{3}\)
9. \(8b^{6}+8b^{4}q+2b^{2}q^2\)
10. \(108x^{11}+36x^{7}+3x^{3}\)
11. \(108b^{7}+180b^{5}y+75b^{3}y^2\)
12. \(-108s^{4}+147s^{2}\)

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

Verbetersleutel

1. \(6a^{6}-12a^{5}+6a^{4}=6a^{4}(a^2-2a+1)=6a^{4}(a-1)^2\)
2. \(180p^{5}-5p^{3}=5p^{3}(36p^{2}-1)=5p^{3}(6p+1)(6p-1)\)
3. \(16a^{5}-56a^{4}+49a^{3}=a^{3}(16a^{2}-56a+49)=a^{3}(4a-7)^2\)
4. \(5x^{4}-125x^{2}=5x^{2}(x^2-25)=5x^{2}(x-5)(x+5)\)
5. \(-245a^{12}-420a^{8}-180a^{4}=-5a^{4}(49a^{8}+84a^4+36)=-5a^{4}(7a^4+6)^2\)
6. \(-18p^{7}+24p^{6}-8p^{5}=-2p^{5}(9p^{2}-12p+4)=-2p^{5}(3p-2)^2\)
7. \(4y^{9}-y^{5}=y^{5}(4y^{4}-1)=y^{5}(2y^2+1)(2y^2-1)\)
8. \(54x^{13}+36x^{8}+6x^{3}=6x^{3}(9x^{10}+6x^5+1)=6x^{3}(3x^5+1)^2\)
9. \(8b^{6}+8b^{4}q+2b^{2}q^2=2b^{2}(4b^{4}+4b^2q+q^2)=2b^{2}(2b^2+q)^2\)
10. \(108x^{11}+36x^{7}+3x^{3}=3x^{3}(36x^{8}+12x^4+1)=3x^{3}(6x^4+1)^2\)
11. \(108b^{7}+180b^{5}y+75b^{3}y^2=3b^{3}(36b^{4}+60b^2y+25y^2)=3b^{3}(6b^2+5y)^2\)
12. \(-108s^{4}+147s^{2}=-3s^{2}(36s^{2}-49)=-3s^{2}(6s+7)(6s-7)\)