Ontbinden in factoren (2)

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

1. \(-75s^{4}+27s^{2}\)
2. \(5a^{6}-320a^{4}\)
3. \(9s^{6}-25s^{4}\)
4. \(-25p^{7}+16p^{5}\)
5. \(48q^{6}+120q^{4}s+75q^{2}s^2\)
6. \(6p^{4}-108p^{3}+486p^{2}\)
7. \(-9s^{12}-6s^{8}y-s^{4}y^2\)
8. \(8b^{8}+8b^{5}y+2b^{2}y^2\)
9. \(20s^{7}+20s^{5}+5s^{3}\)
10. \(-5x^{4}+45x^{2}\)
11. \(-320p^{8}+400p^{5}q-125p^{2}q^2\)
12. \(50x^{4}+120x^{3}+72x^{2}\)

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

Verbetersleutel

1. \(-75s^{4}+27s^{2}=-3s^{2}(25s^{2}-9)=-3s^{2}(5s+3)(5s-3)\)
2. \(5a^{6}-320a^{4}=5a^{4}(a^2-64)=5a^{4}(a+8)(a-8)\)
3. \(9s^{6}-25s^{4}=s^{4}(9s^{2}-25)=s^{4}(3s+5)(3s-5)\)
4. \(-25p^{7}+16p^{5}=-p^{5}(25p^{2}-16)=-p^{5}(5p+4)(5p-4)\)
5. \(48q^{6}+120q^{4}s+75q^{2}s^2=3q^{2}(16q^{4}+40q^2s+25s^2)=3q^{2}(4q^2+5s)^2\)
6. \(6p^{4}-108p^{3}+486p^{2}=6p^{2}(p^2-18p+81)=6p^{2}(p-9)^2\)
7. \(-9s^{12}-6s^{8}y-s^{4}y^2=-s^{4}(9s^{8}+6s^4y+y^2)=-s^{4}(3s^4+y)^2\)
8. \(8b^{8}+8b^{5}y+2b^{2}y^2=2b^{2}(4b^{6}+4b^3y+y^2)=2b^{2}(2b^3+y)^2\)
9. \(20s^{7}+20s^{5}+5s^{3}=5s^{3}(4s^{4}+4s^2+1)=5s^{3}(2s^2+1)^2\)
10. \(-5x^{4}+45x^{2}=-5x^{2}(x^2-9)=-5x^{2}(x-3)(x+3)\)
11. \(-320p^{8}+400p^{5}q-125p^{2}q^2=-5p^{2}(64p^{6}-80p^3q+25q^2)=-5p^{2}(8p^3-5q)^2\)
12. \(50x^{4}+120x^{3}+72x^{2}=2x^{2}(25x^{2}+60x+36)=2x^{2}(5x+6)^2\)