Ontbinden in factoren (2)

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

1. \(-27x^{8}+48x^{2}\)
2. \(-80s^{10}+245s^{4}\)
3. \(-6y^{4}+48y^{3}-96y^{2}\)
4. \(50y^{10}+20y^{7}+2y^{4}\)
5. \(-384b^{6}+480b^{5}-150b^{4}\)
6. \(-2p^{6}+24p^{5}-72p^{4}\)
7. \(6y^{5}+48y^{4}+96y^{3}\)
8. \(-125y^{4}-300y^{3}-180y^{2}\)
9. \(48x^{11}-72x^{8}y+27x^{5}y^2\)
10. \(-18y^{5}+32y^{3}\)
11. \(-50a^{6}+2a^{4}\)
12. \(54b^{12}-294b^{4}\)

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

Verbetersleutel

1. \(-27x^{8}+48x^{2}=-3x^{2}(9x^{6}-16)=-3x^{2}(3x^3+4)(3x^3-4)\)
2. \(-80s^{10}+245s^{4}=-5s^{4}(16s^{6}-49)=-5s^{4}(4s^3+7)(4s^3-7)\)
3. \(-6y^{4}+48y^{3}-96y^{2}=-6y^{2}(y^2-8y+16)=-6y^{2}(y-4)^2\)
4. \(50y^{10}+20y^{7}+2y^{4}=2y^{4}(25y^{6}+10y^3+1)=2y^{4}(5y^3+1)^2\)
5. \(-384b^{6}+480b^{5}-150b^{4}=-6b^{4}(64b^{2}-80b+25)=-6b^{4}(8b-5)^2\)
6. \(-2p^{6}+24p^{5}-72p^{4}=-2p^{4}(p^2-12p+36)=-2p^{4}(p-6)^2\)
7. \(6y^{5}+48y^{4}+96y^{3}=6y^{3}(y^2+8y+16)=6y^{3}(y+4)^2\)
8. \(-125y^{4}-300y^{3}-180y^{2}=-5y^{2}(25y^{2}+60y+36)=-5y^{2}(5y+6)^2\)
9. \(48x^{11}-72x^{8}y+27x^{5}y^2=3x^{5}(16x^{6}-24x^3y+9y^2)=3x^{5}(4x^3-3y)^2\)
10. \(-18y^{5}+32y^{3}=-2y^{3}(9y^{2}-16)=-2y^{3}(3y+4)(3y-4)\)
11. \(-50a^{6}+2a^{4}=-2a^{4}(25a^{2}-1)=-2a^{4}(5a+1)(5a-1)\)
12. \(54b^{12}-294b^{4}=6b^{4}(9b^{8}-49)=6b^{4}(3b^4+7)(3b^4-7)\)