Ontbinden in factoren (2)

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

1. \(80a^{9}+40a^{6}q+5a^{3}q^2\)
2. \(5b^{4}+60b^{3}+180b^{2}\)
3. \(-245y^{10}-420y^{6}-180y^{2}\)
4. \(5b^{4}-245b^{2}\)
5. \(2q^{5}-4q^{4}+2q^{3}\)
6. \(128s^{4}+32s^{3}+2s^{2}\)
7. \(150p^{7}-96p^{5}\)
8. \(-5b^{5}-70b^{4}-245b^{3}\)
9. \(-72q^{8}+2q^{4}\)
10. \(-6a^{4}+54a^{2}\)
11. \(6b^{5}+48b^{4}+96b^{3}\)
12. \(150q^{15}-54q^{3}\)

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

Verbetersleutel

1. \(80a^{9}+40a^{6}q+5a^{3}q^2=5a^{3}(16a^{6}+8a^3q+q^2)=5a^{3}(4a^3+q)^2\)
2. \(5b^{4}+60b^{3}+180b^{2}=5b^{2}(b^2+12b+36)=5b^{2}(b+6)^2\)
3. \(-245y^{10}-420y^{6}-180y^{2}=-5y^{2}(49y^{8}+84y^4+36)=-5y^{2}(7y^4+6)^2\)
4. \(5b^{4}-245b^{2}=5b^{2}(b^2-49)=5b^{2}(b-7)(b+7)\)
5. \(2q^{5}-4q^{4}+2q^{3}=2q^{3}(q^2-2q+1)=2q^{3}(q-1)^2\)
6. \(128s^{4}+32s^{3}+2s^{2}=2s^{2}(64s^{2}+16s+1)=2s^{2}(8s+1)^2\)
7. \(150p^{7}-96p^{5}=6p^{5}(25p^{2}-16)=6p^{5}(5p+4)(5p-4)\)
8. \(-5b^{5}-70b^{4}-245b^{3}=-5b^{3}(b^2+14b+49)=-5b^{3}(b+7)^2\)
9. \(-72q^{8}+2q^{4}=-2q^{4}(36q^{4}-1)=-2q^{4}(6q^2+1)(6q^2-1)\)
10. \(-6a^{4}+54a^{2}=-6a^{2}(a^2-9)=-6a^{2}(a-3)(a+3)\)
11. \(6b^{5}+48b^{4}+96b^{3}=6b^{3}(b^2+8b+16)=6b^{3}(b+4)^2\)
12. \(150q^{15}-54q^{3}=6q^{3}(25q^{12}-9)=6q^{3}(5q^6+3)(5q^6-3)\)