Ontbinden in factoren (2)

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

1. \(80b^{14}+40b^{9}s+5b^{4}s^2\)
2. \(-25b^{12}+49b^{4}\)
3. \(2y^{5}-2y^{3}\)
4. \(-s^{7}-16s^{6}-64s^{5}\)
5. \(32x^{11}-112x^{7}+98x^{3}\)
6. \(-27q^{5}+90q^{4}-75q^{3}\)
7. \(54a^{10}-96a^{2}\)
8. \(3q^{4}-42q^{3}+147q^{2}\)
9. \(64p^{10}+80p^{6}+25p^{2}\)
10. \(6b^{5}-96b^{3}\)
11. \(-16p^{18}+49p^{4}\)
12. \(-2a^{5}+50a^{3}\)

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

Verbetersleutel

1. \(80b^{14}+40b^{9}s+5b^{4}s^2=5b^{4}(16b^{10}+8b^5s+s^2)=5b^{4}(4b^5+s)^2\)
2. \(-25b^{12}+49b^{4}=-b^{4}(25b^{8}-49)=-b^{4}(5b^4+7)(5b^4-7)\)
3. \(2y^{5}-2y^{3}=2y^{3}(y^2-1)=2y^{3}(y-1)(y+1)\)
4. \(-s^{7}-16s^{6}-64s^{5}=-s^{5}(s^2+16s+64)=-s^{5}(s+8)^2\)
5. \(32x^{11}-112x^{7}+98x^{3}=2x^{3}(16x^{8}-56x^4+49)=2x^{3}(4x^4-7)^2\)
6. \(-27q^{5}+90q^{4}-75q^{3}=-3q^{3}(9q^{2}-30q+25)=-3q^{3}(3q-5)^2\)
7. \(54a^{10}-96a^{2}=6a^{2}(9a^{8}-16)=6a^{2}(3a^4+4)(3a^4-4)\)
8. \(3q^{4}-42q^{3}+147q^{2}=3q^{2}(q^2-14q+49)=3q^{2}(q-7)^2\)
9. \(64p^{10}+80p^{6}+25p^{2}=p^{2}(64p^{8}+80p^4+25)=p^{2}(8p^4+5)^2\)
10. \(6b^{5}-96b^{3}=6b^{3}(b^2-16)=6b^{3}(b+4)(b-4)\)
11. \(-16p^{18}+49p^{4}=-p^{4}(16p^{14}-49)=-p^{4}(4p^7+7)(4p^7-7)\)
12. \(-2a^{5}+50a^{3}=-2a^{3}(a^2-25)=-2a^{3}(a-5)(a+5)\)