Ontbinden in factoren (2)

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

1. \(-20q^{18}+45q^{2}\)
2. \(-16b^{11}+24b^{7}x-9b^{3}x^2\)
3. \(-24y^{11}+6y^{3}\)
4. \(-6y^{7}+6y^{5}\)
5. \(20b^{4}+60b^{3}+45b^{2}\)
6. \(-50y^{7}-120y^{6}-72y^{5}\)
7. \(-245a^{13}-70a^{8}-5a^{3}\)
8. \(50x^{5}-2x^{3}\)
9. \(-54y^{19}+24y^{3}\)
10. \(75a^{12}+30a^{8}+3a^{4}\)
11. \(-2x^{6}+24x^{5}-72x^{4}\)
12. \(27y^{8}+72y^{6}+48y^{4}\)

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

Verbetersleutel

1. \(-20q^{18}+45q^{2}=-5q^{2}(4q^{16}-9)=-5q^{2}(2q^8+3)(2q^8-3)\)
2. \(-16b^{11}+24b^{7}x-9b^{3}x^2=-b^{3}(16b^{8}-24b^4x+9x^2)=-b^{3}(4b^4-3x)^2\)
3. \(-24y^{11}+6y^{3}=-6y^{3}(4y^{8}-1)=-6y^{3}(2y^4+1)(2y^4-1)\)
4. \(-6y^{7}+6y^{5}=-6y^{5}(y^2-1)=-6y^{5}(y+1)(y-1)\)
5. \(20b^{4}+60b^{3}+45b^{2}=5b^{2}(4b^{2}+12b+9)=5b^{2}(2b+3)^2\)
6. \(-50y^{7}-120y^{6}-72y^{5}=-2y^{5}(25y^{2}+60y+36)=-2y^{5}(5y+6)^2\)
7. \(-245a^{13}-70a^{8}-5a^{3}=-5a^{3}(49a^{10}+14a^5+1)=-5a^{3}(7a^5+1)^2\)
8. \(50x^{5}-2x^{3}=2x^{3}(25x^{2}-1)=2x^{3}(5x+1)(5x-1)\)
9. \(-54y^{19}+24y^{3}=-6y^{3}(9y^{16}-4)=-6y^{3}(3y^8+2)(3y^8-2)\)
10. \(75a^{12}+30a^{8}+3a^{4}=3a^{4}(25a^{8}+10a^4+1)=3a^{4}(5a^4+1)^2\)
11. \(-2x^{6}+24x^{5}-72x^{4}=-2x^{4}(x^2-12x+36)=-2x^{4}(x-6)^2\)
12. \(27y^{8}+72y^{6}+48y^{4}=3y^{4}(9y^{4}+24y^2+16)=3y^{4}(3y^2+4)^2\)