Ontbinden in factoren (2)

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

1. \(18a^{10}+12a^{7}+2a^{4}\)
2. \(98p^{9}+84p^{7}y+18p^{5}y^2\)
3. \(4q^{15}-q^{5}\)
4. \(108q^{6}-147q^{4}\)
5. \(-27s^{12}+3s^{4}\)
6. \(-320y^{5}-80y^{4}-5y^{3}\)
7. \(27a^{7}+126a^{6}+147a^{5}\)
8. \(-245b^{6}-560b^{5}-320b^{4}\)
9. \(-180s^{6}+245s^{4}\)
10. \(8x^{4}+56x^{3}+98x^{2}\)
11. \(-36a^{13}+25a^{5}\)
12. \(-2p^{5}+18p^{3}\)

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

Verbetersleutel

1. \(18a^{10}+12a^{7}+2a^{4}=2a^{4}(9a^{6}+6a^3+1)=2a^{4}(3a^3+1)^2\)
2. \(98p^{9}+84p^{7}y+18p^{5}y^2=2p^{5}(49p^{4}+42p^2y+9y^2)=2p^{5}(7p^2+3y)^2\)
3. \(4q^{15}-q^{5}=q^{5}(4q^{10}-1)=q^{5}(2q^5+1)(2q^5-1)\)
4. \(108q^{6}-147q^{4}=3q^{4}(36q^{2}-49)=3q^{4}(6q+7)(6q-7)\)
5. \(-27s^{12}+3s^{4}=-3s^{4}(9s^{8}-1)=-3s^{4}(3s^4+1)(3s^4-1)\)
6. \(-320y^{5}-80y^{4}-5y^{3}=-5y^{3}(64y^{2}+16y+1)=-5y^{3}(8y+1)^2\)
7. \(27a^{7}+126a^{6}+147a^{5}=3a^{5}(9a^{2}+42a+49)=3a^{5}(3a+7)^2\)
8. \(-245b^{6}-560b^{5}-320b^{4}=-5b^{4}(49b^{2}+112b+64)=-5b^{4}(7b+8)^2\)
9. \(-180s^{6}+245s^{4}=-5s^{4}(36s^{2}-49)=-5s^{4}(6s+7)(6s-7)\)
10. \(8x^{4}+56x^{3}+98x^{2}=2x^{2}(4x^{2}+28x+49)=2x^{2}(2x+7)^2\)
11. \(-36a^{13}+25a^{5}=-a^{5}(36a^{8}-25)=-a^{5}(6a^4+5)(6a^4-5)\)
12. \(-2p^{5}+18p^{3}=-2p^{3}(p^2-9)=-2p^{3}(p+3)(p-3)\)