Ontbinden in factoren (2)

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

1. \(9y^{11}-y^{3}\)
2. \(-54p^{17}+96p^{5}\)
3. \(-6y^{6}-12y^{5}-6y^{4}\)
4. \(-18q^{16}+98q^{4}\)
5. \(-4p^{8}+p^{2}\)
6. \(150s^{10}+180s^{6}+54s^{2}\)
7. \(-6q^{5}+294q^{3}\)
8. \(-294x^{6}-420x^{5}-150x^{4}\)
9. \(294x^{6}+84x^{5}+6x^{4}\)
10. \(-5a^{4}+80a^{2}\)
11. \(54q^{10}-180q^{7}y+150q^{4}y^2\)
12. \(b^{7}-64b^{5}\)

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

Verbetersleutel

1. \(9y^{11}-y^{3}=y^{3}(9y^{8}-1)=y^{3}(3y^4+1)(3y^4-1)\)
2. \(-54p^{17}+96p^{5}=-6p^{5}(9p^{12}-16)=-6p^{5}(3p^6+4)(3p^6-4)\)
3. \(-6y^{6}-12y^{5}-6y^{4}=-6y^{4}(y^2+2y+1)=-6y^{4}(y+1)^2\)
4. \(-18q^{16}+98q^{4}=-2q^{4}(9q^{12}-49)=-2q^{4}(3q^6+7)(3q^6-7)\)
5. \(-4p^{8}+p^{2}=-p^{2}(4p^{6}-1)=-p^{2}(2p^3+1)(2p^3-1)\)
6. \(150s^{10}+180s^{6}+54s^{2}=6s^{2}(25s^{8}+30s^4+9)=6s^{2}(5s^4+3)^2\)
7. \(-6q^{5}+294q^{3}=-6q^{3}(q^2-49)=-6q^{3}(q+7)(q-7)\)
8. \(-294x^{6}-420x^{5}-150x^{4}=-6x^{4}(49x^{2}+70x+25)=-6x^{4}(7x+5)^2\)
9. \(294x^{6}+84x^{5}+6x^{4}=6x^{4}(49x^{2}+14x+1)=6x^{4}(7x+1)^2\)
10. \(-5a^{4}+80a^{2}=-5a^{2}(a^2-16)=-5a^{2}(a+4)(a-4)\)
11. \(54q^{10}-180q^{7}y+150q^{4}y^2=6q^{4}(9q^{6}-30q^3y+25y^2)=6q^{4}(3q^3-5y)^2\)
12. \(b^{7}-64b^{5}=b^{5}(b^2-64)=b^{5}(b+8)(b-8)\)