Ontbinden in factoren (2)

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

1. \(y^{4}+6y^{3}+9y^{2}\)
2. \(150a^{9}+60a^{6}b+6a^{3}b^2\)
3. \(98a^{12}-168a^{8}+72a^{4}\)
4. \(24p^{8}+24p^{6}+6p^{4}\)
5. \(-180b^{5}+245b^{3}\)
6. \(-20p^{20}+125p^{4}\)
7. \(-12x^{5}-12x^{4}-3x^{3}\)
8. \(-50a^{7}-120a^{6}-72a^{5}\)
9. \(-320p^{14}-80p^{9}-5p^{4}\)
10. \(-3q^{6}+27q^{4}\)
11. \(-72b^{9}+120b^{6}y-50b^{3}y^2\)
12. \(-72y^{9}-24y^{7}-2y^{5}\)

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

Verbetersleutel

1. \(y^{4}+6y^{3}+9y^{2}=y^{2}(y^2+6y+9)=y^{2}(y+3)^2\)
2. \(150a^{9}+60a^{6}b+6a^{3}b^2=6a^{3}(25a^{6}+10a^3b+b^2)=6a^{3}(5a^3+b)^2\)
3. \(98a^{12}-168a^{8}+72a^{4}=2a^{4}(49a^{8}-84a^4+36)=2a^{4}(7a^4-6)^2\)
4. \(24p^{8}+24p^{6}+6p^{4}=6p^{4}(4p^{4}+4p^2+1)=6p^{4}(2p^2+1)^2\)
5. \(-180b^{5}+245b^{3}=-5b^{3}(36b^{2}-49)=-5b^{3}(6b+7)(6b-7)\)
6. \(-20p^{20}+125p^{4}=-5p^{4}(4p^{16}-25)=-5p^{4}(2p^8+5)(2p^8-5)\)
7. \(-12x^{5}-12x^{4}-3x^{3}=-3x^{3}(4x^{2}+4x+1)=-3x^{3}(2x+1)^2\)
8. \(-50a^{7}-120a^{6}-72a^{5}=-2a^{5}(25a^{2}+60a+36)=-2a^{5}(5a+6)^2\)
9. \(-320p^{14}-80p^{9}-5p^{4}=-5p^{4}(64p^{10}+16p^5+1)=-5p^{4}(8p^5+1)^2\)
10. \(-3q^{6}+27q^{4}=-3q^{4}(q^2-9)=-3q^{4}(q-3)(q+3)\)
11. \(-72b^{9}+120b^{6}y-50b^{3}y^2=-2b^{3}(36b^{6}-60b^3y+25y^2)=-2b^{3}(6b^3-5y)^2\)
12. \(-72y^{9}-24y^{7}-2y^{5}=-2y^{5}(36y^{4}+12y^2+1)=-2y^{5}(6y^2+1)^2\)