Ontbinden in factoren (2)

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

1. \(8a^{8}+8a^{6}+2a^{4}\)
2. \(-16q^{12}+56q^{7}x-49q^{2}x^2\)
3. \(-6y^{5}+84y^{4}-294y^{3}\)
4. \(180y^{5}-300y^{4}+125y^{3}\)
5. \(-4p^{19}+25p^{5}\)
6. \(-16y^{16}+49y^{4}\)
7. \(-8a^{6}-56a^{5}-98a^{4}\)
8. \(-80q^{6}+45q^{4}\)
9. \(18p^{4}-24p^{3}+8p^{2}\)
10. \(150b^{15}-54b^{3}\)
11. \(-108b^{5}+75b^{3}\)
12. \(-6p^{4}+150p^{2}\)

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

Verbetersleutel

1. \(8a^{8}+8a^{6}+2a^{4}=2a^{4}(4a^{4}+4a^2+1)=2a^{4}(2a^2+1)^2\)
2. \(-16q^{12}+56q^{7}x-49q^{2}x^2=-q^{2}(16q^{10}-56q^5x+49x^2)=-q^{2}(4q^5-7x)^2\)
3. \(-6y^{5}+84y^{4}-294y^{3}=-6y^{3}(y^2-14y+49)=-6y^{3}(y-7)^2\)
4. \(180y^{5}-300y^{4}+125y^{3}=5y^{3}(36y^{2}-60y+25)=5y^{3}(6y-5)^2\)
5. \(-4p^{19}+25p^{5}=-p^{5}(4p^{14}-25)=-p^{5}(2p^7+5)(2p^7-5)\)
6. \(-16y^{16}+49y^{4}=-y^{4}(16y^{12}-49)=-y^{4}(4y^6+7)(4y^6-7)\)
7. \(-8a^{6}-56a^{5}-98a^{4}=-2a^{4}(4a^{2}+28a+49)=-2a^{4}(2a+7)^2\)
8. \(-80q^{6}+45q^{4}=-5q^{4}(16q^{2}-9)=-5q^{4}(4q+3)(4q-3)\)
9. \(18p^{4}-24p^{3}+8p^{2}=2p^{2}(9p^{2}-12p+4)=2p^{2}(3p-2)^2\)
10. \(150b^{15}-54b^{3}=6b^{3}(25b^{12}-9)=6b^{3}(5b^6+3)(5b^6-3)\)
11. \(-108b^{5}+75b^{3}=-3b^{3}(36b^{2}-25)=-3b^{3}(6b+5)(6b-5)\)
12. \(-6p^{4}+150p^{2}=-6p^{2}(p^2-25)=-6p^{2}(p+5)(p-5)\)