Ontbinden in factoren (2)

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

1. \(-128q^{6}-32q^{4}y-2q^{2}y^2\)
2. \(-48q^{4}+147q^{2}\)
3. \(108s^{8}+180s^{5}+75s^{2}\)
4. \(-3q^{6}+18q^{5}-27q^{4}\)
5. \(24x^{7}+168x^{6}+294x^{5}\)
6. \(2y^{4}-98y^{2}\)
7. \(5q^{4}-5q^{2}\)
8. \(75a^{8}+180a^{5}+108a^{2}\)
9. \(54b^{16}-24b^{4}\)
10. \(-48s^{8}+147s^{2}\)
11. \(4s^{13}+4s^{9}x+s^{5}x^2\)
12. \(125p^{12}+300p^{7}q+180p^{2}q^2\)

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

Verbetersleutel

1. \(-128q^{6}-32q^{4}y-2q^{2}y^2=-2q^{2}(64q^{4}+16q^2y+y^2)=-2q^{2}(8q^2+y)^2\)
2. \(-48q^{4}+147q^{2}=-3q^{2}(16q^{2}-49)=-3q^{2}(4q+7)(4q-7)\)
3. \(108s^{8}+180s^{5}+75s^{2}=3s^{2}(36s^{6}+60s^3+25)=3s^{2}(6s^3+5)^2\)
4. \(-3q^{6}+18q^{5}-27q^{4}=-3q^{4}(q^2-6q+9)=-3q^{4}(q-3)^2\)
5. \(24x^{7}+168x^{6}+294x^{5}=6x^{5}(4x^{2}+28x+49)=6x^{5}(2x+7)^2\)
6. \(2y^{4}-98y^{2}=2y^{2}(y^2-49)=2y^{2}(y+7)(y-7)\)
7. \(5q^{4}-5q^{2}=5q^{2}(q^2-1)=5q^{2}(q-1)(q+1)\)
8. \(75a^{8}+180a^{5}+108a^{2}=3a^{2}(25a^{6}+60a^3+36)=3a^{2}(5a^3+6)^2\)
9. \(54b^{16}-24b^{4}=6b^{4}(9b^{12}-4)=6b^{4}(3b^6+2)(3b^6-2)\)
10. \(-48s^{8}+147s^{2}=-3s^{2}(16s^{6}-49)=-3s^{2}(4s^3+7)(4s^3-7)\)
11. \(4s^{13}+4s^{9}x+s^{5}x^2=s^{5}(4s^{8}+4s^4x+x^2)=s^{5}(2s^4+x)^2\)
12. \(125p^{12}+300p^{7}q+180p^{2}q^2=5p^{2}(25p^{10}+60p^5q+36q^2)=5p^{2}(5p^5+6q)^2\)