Ontbinden in factoren (2)

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

1. \(-54a^{4}+72a^{3}-24a^{2}\)
2. \(6a^{6}+24a^{5}+24a^{4}\)
3. \(16b^{8}-56b^{6}y+49b^{4}y^2\)
4. \(5y^{5}-320y^{3}\)
5. \(-192p^{4}+240p^{3}-75p^{2}\)
6. \(-216x^{8}+294x^{4}\)
7. \(125a^{6}-5a^{4}\)
8. \(108a^{7}+36a^{5}x+3a^{3}x^2\)
9. \(48p^{12}-72p^{8}+27p^{4}\)
10. \(5s^{5}-5s^{3}\)
11. \(5s^{4}-80s^{2}\)
12. \(-80b^{4}+245b^{2}\)

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

Verbetersleutel

1. \(-54a^{4}+72a^{3}-24a^{2}=-6a^{2}(9a^{2}-12a+4)=-6a^{2}(3a-2)^2\)
2. \(6a^{6}+24a^{5}+24a^{4}=6a^{4}(a^2+4a+4)=6a^{4}(a+2)^2\)
3. \(16b^{8}-56b^{6}y+49b^{4}y^2=b^{4}(16b^{4}-56b^2y+49y^2)=b^{4}(4b^2-7y)^2\)
4. \(5y^{5}-320y^{3}=5y^{3}(y^2-64)=5y^{3}(y-8)(y+8)\)
5. \(-192p^{4}+240p^{3}-75p^{2}=-3p^{2}(64p^{2}-80p+25)=-3p^{2}(8p-5)^2\)
6. \(-216x^{8}+294x^{4}=-6x^{4}(36x^{4}-49)=-6x^{4}(6x^2+7)(6x^2-7)\)
7. \(125a^{6}-5a^{4}=5a^{4}(25a^{2}-1)=5a^{4}(5a+1)(5a-1)\)
8. \(108a^{7}+36a^{5}x+3a^{3}x^2=3a^{3}(36a^{4}+12a^2x+x^2)=3a^{3}(6a^2+x)^2\)
9. \(48p^{12}-72p^{8}+27p^{4}=3p^{4}(16p^{8}-24p^4+9)=3p^{4}(4p^4-3)^2\)
10. \(5s^{5}-5s^{3}=5s^{3}(s^2-1)=5s^{3}(s+1)(s-1)\)
11. \(5s^{4}-80s^{2}=5s^{2}(s^2-16)=5s^{2}(s-4)(s+4)\)
12. \(-80b^{4}+245b^{2}=-5b^{2}(16b^{2}-49)=-5b^{2}(4b+7)(4b-7)\)