Ontbinden in factoren (2)

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

1. \(45b^{8}+60b^{6}q+20b^{4}q^2\)
2. \(-5x^{5}+320x^{3}\)
3. \(80s^{5}-45s^{3}\)
4. \(-108y^{6}+75y^{4}\)
5. \(245p^{5}+560p^{4}+320p^{3}\)
6. \(192p^{9}+48p^{6}q+3p^{3}q^2\)
7. \(20x^{15}-45x^{3}\)
8. \(5q^{5}-40q^{4}+80q^{3}\)
9. \(5q^{5}+10q^{4}+5q^{3}\)
10. \(-y^{7}-2y^{6}-y^{5}\)
11. \(-8a^{11}-8a^{7}x-2a^{3}x^2\)
12. \(98p^{9}+28p^{6}s+2p^{3}s^2\)

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

Verbetersleutel

1. \(45b^{8}+60b^{6}q+20b^{4}q^2=5b^{4}(9b^{4}+12b^2q+4q^2)=5b^{4}(3b^2+2q)^2\)
2. \(-5x^{5}+320x^{3}=-5x^{3}(x^2-64)=-5x^{3}(x-8)(x+8)\)
3. \(80s^{5}-45s^{3}=5s^{3}(16s^{2}-9)=5s^{3}(4s+3)(4s-3)\)
4. \(-108y^{6}+75y^{4}=-3y^{4}(36y^{2}-25)=-3y^{4}(6y+5)(6y-5)\)
5. \(245p^{5}+560p^{4}+320p^{3}=5p^{3}(49p^{2}+112p+64)=5p^{3}(7p+8)^2\)
6. \(192p^{9}+48p^{6}q+3p^{3}q^2=3p^{3}(64p^{6}+16p^3q+q^2)=3p^{3}(8p^3+q)^2\)
7. \(20x^{15}-45x^{3}=5x^{3}(4x^{12}-9)=5x^{3}(2x^6+3)(2x^6-3)\)
8. \(5q^{5}-40q^{4}+80q^{3}=5q^{3}(q^2-8q+16)=5q^{3}(q-4)^2\)
9. \(5q^{5}+10q^{4}+5q^{3}=5q^{3}(q^2+2q+1)=5q^{3}(q+1)^2\)
10. \(-y^{7}-2y^{6}-y^{5}=-y^{5}(y^2+2y+1)=-y^{5}(y+1)^2\)
11. \(-8a^{11}-8a^{7}x-2a^{3}x^2=-2a^{3}(4a^{8}+4a^4x+x^2)=-2a^{3}(2a^4+x)^2\)
12. \(98p^{9}+28p^{6}s+2p^{3}s^2=2p^{3}(49p^{6}+14p^3s+s^2)=2p^{3}(7p^3+s)^2\)