Ontbinden in factoren (2)

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

1. \(-54y^{8}+180y^{5}-150y^{2}\)
2. \(245x^{12}-420x^{7}y+180x^{2}y^2\)
3. \(-150y^{13}+120y^{9}-24y^{5}\)
4. \(12a^{5}-3a^{3}\)
5. \(5b^{6}+20b^{5}+20b^{4}\)
6. \(-4x^{5}-28x^{4}-49x^{3}\)
7. \(96x^{10}+48x^{6}y+6x^{2}y^2\)
8. \(-50a^{10}-20a^{7}-2a^{4}\)
9. \(-36q^{13}-60q^{9}-25q^{5}\)
10. \(-72b^{12}-24b^{8}x-2b^{4}x^2\)
11. \(8x^{4}-2x^{2}\)
12. \(54q^{11}+72q^{8}+24q^{5}\)

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

Verbetersleutel

1. \(-54y^{8}+180y^{5}-150y^{2}=-6y^{2}(9y^{6}-30y^3+25)=-6y^{2}(3y^3-5)^2\)
2. \(245x^{12}-420x^{7}y+180x^{2}y^2=5x^{2}(49x^{10}-84x^5y+36y^2)=5x^{2}(7x^5-6y)^2\)
3. \(-150y^{13}+120y^{9}-24y^{5}=-6y^{5}(25y^{8}-20y^4+4)=-6y^{5}(5y^4-2)^2\)
4. \(12a^{5}-3a^{3}=3a^{3}(4a^{2}-1)=3a^{3}(2a+1)(2a-1)\)
5. \(5b^{6}+20b^{5}+20b^{4}=5b^{4}(b^2+4b+4)=5b^{4}(b+2)^2\)
6. \(-4x^{5}-28x^{4}-49x^{3}=-x^{3}(4x^{2}+28x+49)=-x^{3}(2x+7)^2\)
7. \(96x^{10}+48x^{6}y+6x^{2}y^2=6x^{2}(16x^{8}+8x^4y+y^2)=6x^{2}(4x^4+y)^2\)
8. \(-50a^{10}-20a^{7}-2a^{4}=-2a^{4}(25a^{6}+10a^3+1)=-2a^{4}(5a^3+1)^2\)
9. \(-36q^{13}-60q^{9}-25q^{5}=-q^{5}(36q^{8}+60q^4+25)=-q^{5}(6q^4+5)^2\)
10. \(-72b^{12}-24b^{8}x-2b^{4}x^2=-2b^{4}(36b^{8}+12b^4x+x^2)=-2b^{4}(6b^4+x)^2\)
11. \(8x^{4}-2x^{2}=2x^{2}(4x^{2}-1)=2x^{2}(2x+1)(2x-1)\)
12. \(54q^{11}+72q^{8}+24q^{5}=6q^{5}(9q^{6}+12q^3+4)=6q^{5}(3q^3+2)^2\)