Ontbinden in factoren (2)

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

1. \(150a^{13}-420a^{8}y+294a^{3}y^2\)
2. \(45b^{6}+120b^{5}+80b^{4}\)
3. \(-80q^{8}+245q^{2}\)
4. \(-2b^{5}+20b^{4}-50b^{3}\)
5. \(-45b^{7}+5b^{5}\)
6. \(96q^{10}-144q^{7}+54q^{4}\)
7. \(-16y^{5}-8y^{4}-y^{3}\)
8. \(16s^{11}-25s^{3}\)
9. \(16b^{6}-b^{4}\)
10. \(27q^{11}-12q^{5}\)
11. \(-2s^{7}+50s^{5}\)
12. \(2b^{7}-16b^{6}+32b^{5}\)

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

Verbetersleutel

1. \(150a^{13}-420a^{8}y+294a^{3}y^2=6a^{3}(25a^{10}-70a^5y+49y^2)=6a^{3}(5a^5-7y)^2\)
2. \(45b^{6}+120b^{5}+80b^{4}=5b^{4}(9b^{2}+24b+16)=5b^{4}(3b+4)^2\)
3. \(-80q^{8}+245q^{2}=-5q^{2}(16q^{6}-49)=-5q^{2}(4q^3+7)(4q^3-7)\)
4. \(-2b^{5}+20b^{4}-50b^{3}=-2b^{3}(b^2-10b+25)=-2b^{3}(b-5)^2\)
5. \(-45b^{7}+5b^{5}=-5b^{5}(9b^{2}-1)=-5b^{5}(3b+1)(3b-1)\)
6. \(96q^{10}-144q^{7}+54q^{4}=6q^{4}(16q^{6}-24q^3+9)=6q^{4}(4q^3-3)^2\)
7. \(-16y^{5}-8y^{4}-y^{3}=-y^{3}(16y^{2}+8y+1)=-y^{3}(4y+1)^2\)
8. \(16s^{11}-25s^{3}=s^{3}(16s^{8}-25)=s^{3}(4s^4+5)(4s^4-5)\)
9. \(16b^{6}-b^{4}=b^{4}(16b^{2}-1)=b^{4}(4b+1)(4b-1)\)
10. \(27q^{11}-12q^{5}=3q^{5}(9q^{6}-4)=3q^{5}(3q^3+2)(3q^3-2)\)
11. \(-2s^{7}+50s^{5}=-2s^{5}(s^2-25)=-2s^{5}(s+5)(s-5)\)
12. \(2b^{7}-16b^{6}+32b^{5}=2b^{5}(b^2-8b+16)=2b^{5}(b-4)^2\)