Ontbinden in factoren (2)

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

1. \(5a^{6}-80a^{5}+320a^{4}\)
2. \(-2y^{5}+18y^{3}\)
3. \(20q^{16}-45q^{4}\)
4. \(147p^{4}+336p^{3}+192p^{2}\)
5. \(-a^{5}+16a^{3}\)
6. \(-32y^{10}+48y^{7}-18y^{4}\)
7. \(48q^{12}-75q^{2}\)
8. \(2x^{7}+8x^{6}+8x^{5}\)
9. \(24b^{13}+24b^{9}+6b^{5}\)
10. \(216x^{4}-150x^{2}\)
11. \(36b^{13}-60b^{9}y+25b^{5}y^2\)
12. \(s^{7}-49s^{5}\)

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

Verbetersleutel

1. \(5a^{6}-80a^{5}+320a^{4}=5a^{4}(a^2-16a+64)=5a^{4}(a-8)^2\)
2. \(-2y^{5}+18y^{3}=-2y^{3}(y^2-9)=-2y^{3}(y-3)(y+3)\)
3. \(20q^{16}-45q^{4}=5q^{4}(4q^{12}-9)=5q^{4}(2q^6+3)(2q^6-3)\)
4. \(147p^{4}+336p^{3}+192p^{2}=3p^{2}(49p^{2}+112p+64)=3p^{2}(7p+8)^2\)
5. \(-a^{5}+16a^{3}=-a^{3}(a^2-16)=-a^{3}(a+4)(a-4)\)
6. \(-32y^{10}+48y^{7}-18y^{4}=-2y^{4}(16y^{6}-24y^3+9)=-2y^{4}(4y^3-3)^2\)
7. \(48q^{12}-75q^{2}=3q^{2}(16q^{10}-25)=3q^{2}(4q^5+5)(4q^5-5)\)
8. \(2x^{7}+8x^{6}+8x^{5}=2x^{5}(x^2+4x+4)=2x^{5}(x+2)^2\)
9. \(24b^{13}+24b^{9}+6b^{5}=6b^{5}(4b^{8}+4b^4+1)=6b^{5}(2b^4+1)^2\)
10. \(216x^{4}-150x^{2}=6x^{2}(36x^{2}-25)=6x^{2}(6x+5)(6x-5)\)
11. \(36b^{13}-60b^{9}y+25b^{5}y^2=b^{5}(36b^{8}-60b^4y+25y^2)=b^{5}(6b^4-5y)^2\)
12. \(s^{7}-49s^{5}=s^{5}(s^2-49)=s^{5}(s-7)(s+7)\)