Ontbinden in factoren (2)

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

1. \(-8y^{7}+18y^{5}\)
2. \(-48b^{14}+72b^{9}-27b^{4}\)
3. \(2y^{4}-8y^{3}+8y^{2}\)
4. \(-9y^{7}+49y^{5}\)
5. \(-150a^{7}+54a^{5}\)
6. \(y^{7}+2y^{6}+y^{5}\)
7. \(150a^{5}-120a^{4}+24a^{3}\)
8. \(9y^{10}-30y^{7}+25y^{4}\)
9. \(-3x^{5}+18x^{4}-27x^{3}\)
10. \(27p^{5}+72p^{4}+48p^{3}\)
11. \(180q^{12}+60q^{7}y+5q^{2}y^2\)
12. \(80a^{12}+120a^{8}y+45a^{4}y^2\)

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

Verbetersleutel

1. \(-8y^{7}+18y^{5}=-2y^{5}(4y^{2}-9)=-2y^{5}(2y+3)(2y-3)\)
2. \(-48b^{14}+72b^{9}-27b^{4}=-3b^{4}(16b^{10}-24b^5+9)=-3b^{4}(4b^5-3)^2\)
3. \(2y^{4}-8y^{3}+8y^{2}=2y^{2}(y^2-4y+4)=2y^{2}(y-2)^2\)
4. \(-9y^{7}+49y^{5}=-y^{5}(9y^{2}-49)=-y^{5}(3y+7)(3y-7)\)
5. \(-150a^{7}+54a^{5}=-6a^{5}(25a^{2}-9)=-6a^{5}(5a+3)(5a-3)\)
6. \(y^{7}+2y^{6}+y^{5}=y^{5}(y^2+2y+1)=y^{5}(y+1)^2\)
7. \(150a^{5}-120a^{4}+24a^{3}=6a^{3}(25a^{2}-20a+4)=6a^{3}(5a-2)^2\)
8. \(9y^{10}-30y^{7}+25y^{4}=y^{4}(9y^{6}-30y^3+25)=y^{4}(3y^3-5)^2\)
9. \(-3x^{5}+18x^{4}-27x^{3}=-3x^{3}(x^2-6x+9)=-3x^{3}(x-3)^2\)
10. \(27p^{5}+72p^{4}+48p^{3}=3p^{3}(9p^{2}+24p+16)=3p^{3}(3p+4)^2\)
11. \(180q^{12}+60q^{7}y+5q^{2}y^2=5q^{2}(36q^{10}+12q^5y+y^2)=5q^{2}(6q^5+y)^2\)
12. \(80a^{12}+120a^{8}y+45a^{4}y^2=5a^{4}(16a^{8}+24a^4y+9y^2)=5a^{4}(4a^4+3y)^2\)