Ontbinden in factoren (2)

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

1. \(-3p^{5}+12p^{4}-12p^{3}\)
2. \(-3b^{6}-18b^{5}-27b^{4}\)
3. \(-245q^{8}-420q^{6}-180q^{4}\)
4. \(-4a^{9}-28a^{6}s-49a^{3}s^2\)
5. \(-294y^{7}-420y^{6}-150y^{5}\)
6. \(-3a^{6}+192a^{4}\)
7. \(3y^{6}-12y^{4}\)
8. \(20b^{11}+140b^{8}p+245b^{5}p^2\)
9. \(12b^{7}+60b^{5}+75b^{3}\)
10. \(y^{6}-25y^{4}\)
11. \(3y^{6}-48y^{4}\)
12. \(x^{5}+12x^{4}+36x^{3}\)

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

Verbetersleutel

1. \(-3p^{5}+12p^{4}-12p^{3}=-3p^{3}(p^2-4p+4)=-3p^{3}(p-2)^2\)
2. \(-3b^{6}-18b^{5}-27b^{4}=-3b^{4}(b^2+6b+9)=-3b^{4}(b+3)^2\)
3. \(-245q^{8}-420q^{6}-180q^{4}=-5q^{4}(49q^{4}+84q^2+36)=-5q^{4}(7q^2+6)^2\)
4. \(-4a^{9}-28a^{6}s-49a^{3}s^2=-a^{3}(4a^{6}+28a^3s+49s^2)=-a^{3}(2a^3+7s)^2\)
5. \(-294y^{7}-420y^{6}-150y^{5}=-6y^{5}(49y^{2}+70y+25)=-6y^{5}(7y+5)^2\)
6. \(-3a^{6}+192a^{4}=-3a^{4}(a^2-64)=-3a^{4}(a+8)(a-8)\)
7. \(3y^{6}-12y^{4}=3y^{4}(y^2-4)=3y^{4}(y-2)(y+2)\)
8. \(20b^{11}+140b^{8}p+245b^{5}p^2=5b^{5}(4b^{6}+28b^3p+49p^2)=5b^{5}(2b^3+7p)^2\)
9. \(12b^{7}+60b^{5}+75b^{3}=3b^{3}(4b^{4}+20b^2+25)=3b^{3}(2b^2+5)^2\)
10. \(y^{6}-25y^{4}=y^{4}(y^2-25)=y^{4}(y-5)(y+5)\)
11. \(3y^{6}-48y^{4}=3y^{4}(y^2-16)=3y^{4}(y-4)(y+4)\)
12. \(x^{5}+12x^{4}+36x^{3}=x^{3}(x^2+12x+36)=x^{3}(x+6)^2\)