Ontbinden in factoren (2)

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

1. \(6a^{6}-12a^{5}+6a^{4}\)
2. \(216p^{4}+504p^{3}+294p^{2}\)
3. \(-8q^{4}+18q^{2}\)
4. \(-25q^{11}+40q^{8}y-16q^{5}y^2\)
5. \(-108a^{9}-36a^{7}p-3a^{5}p^2\)
6. \(64b^{5}+80b^{4}+25b^{3}\)
7. \(-3b^{4}+24b^{3}-48b^{2}\)
8. \(25y^{7}-4y^{5}\)
9. \(6b^{5}-24b^{3}\)
10. \(180q^{7}+420q^{6}+245q^{5}\)
11. \(5s^{7}-320s^{5}\)
12. \(8q^{18}-98q^{4}\)

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

Verbetersleutel

1. \(6a^{6}-12a^{5}+6a^{4}=6a^{4}(a^2-2a+1)=6a^{4}(a-1)^2\)
2. \(216p^{4}+504p^{3}+294p^{2}=6p^{2}(36p^{2}+84p+49)=6p^{2}(6p+7)^2\)
3. \(-8q^{4}+18q^{2}=-2q^{2}(4q^{2}-9)=-2q^{2}(2q+3)(2q-3)\)
4. \(-25q^{11}+40q^{8}y-16q^{5}y^2=-q^{5}(25q^{6}-40q^3y+16y^2)=-q^{5}(5q^3-4y)^2\)
5. \(-108a^{9}-36a^{7}p-3a^{5}p^2=-3a^{5}(36a^{4}+12a^2p+p^2)=-3a^{5}(6a^2+p)^2\)
6. \(64b^{5}+80b^{4}+25b^{3}=b^{3}(64b^{2}+80b+25)=b^{3}(8b+5)^2\)
7. \(-3b^{4}+24b^{3}-48b^{2}=-3b^{2}(b^2-8b+16)=-3b^{2}(b-4)^2\)
8. \(25y^{7}-4y^{5}=y^{5}(25y^{2}-4)=y^{5}(5y+2)(5y-2)\)
9. \(6b^{5}-24b^{3}=6b^{3}(b^2-4)=6b^{3}(b+2)(b-2)\)
10. \(180q^{7}+420q^{6}+245q^{5}=5q^{5}(36q^{2}+84q+49)=5q^{5}(6q+7)^2\)
11. \(5s^{7}-320s^{5}=5s^{5}(s^2-64)=5s^{5}(s-8)(s+8)\)
12. \(8q^{18}-98q^{4}=2q^{4}(4q^{14}-49)=2q^{4}(2q^7+7)(2q^7-7)\)