Ontbinden in factoren (2)

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

1. \(98y^{8}-84y^{5}+18y^{2}\)
2. \(-72y^{7}+50y^{5}\)
3. \(-b^{7}+2b^{6}-b^{5}\)
4. \(-3p^{5}-54p^{4}-243p^{3}\)
5. \(-32a^{11}-80a^{7}b-50a^{3}b^2\)
6. \(80p^{7}+280p^{6}+245p^{5}\)
7. \(-320a^{14}-80a^{9}q-5a^{4}q^2\)
8. \(-6x^{7}-84x^{6}-294x^{5}\)
9. \(-147b^{10}-252b^{7}q-108b^{4}q^2\)
10. \(80a^{6}+120a^{5}+45a^{4}\)
11. \(8x^{13}+8x^{8}+2x^{3}\)
12. \(75a^{5}+180a^{4}+108a^{3}\)

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

Verbetersleutel

1. \(98y^{8}-84y^{5}+18y^{2}=2y^{2}(49y^{6}-42y^3+9)=2y^{2}(7y^3-3)^2\)
2. \(-72y^{7}+50y^{5}=-2y^{5}(36y^{2}-25)=-2y^{5}(6y+5)(6y-5)\)
3. \(-b^{7}+2b^{6}-b^{5}=-b^{5}(b^2-2b+1)=-b^{5}(b-1)^2\)
4. \(-3p^{5}-54p^{4}-243p^{3}=-3p^{3}(p^2+18p+81)=-3p^{3}(p+9)^2\)
5. \(-32a^{11}-80a^{7}b-50a^{3}b^2=-2a^{3}(16a^{8}+40a^4b+25b^2)=-2a^{3}(4a^4+5b)^2\)
6. \(80p^{7}+280p^{6}+245p^{5}=5p^{5}(16p^{2}+56p+49)=5p^{5}(4p+7)^2\)
7. \(-320a^{14}-80a^{9}q-5a^{4}q^2=-5a^{4}(64a^{10}+16a^5q+q^2)=-5a^{4}(8a^5+q)^2\)
8. \(-6x^{7}-84x^{6}-294x^{5}=-6x^{5}(x^2+14x+49)=-6x^{5}(x+7)^2\)
9. \(-147b^{10}-252b^{7}q-108b^{4}q^2=-3b^{4}(49b^{6}+84b^3q+36q^2)=-3b^{4}(7b^3+6q)^2\)
10. \(80a^{6}+120a^{5}+45a^{4}=5a^{4}(16a^{2}+24a+9)=5a^{4}(4a+3)^2\)
11. \(8x^{13}+8x^{8}+2x^{3}=2x^{3}(4x^{10}+4x^5+1)=2x^{3}(2x^5+1)^2\)
12. \(75a^{5}+180a^{4}+108a^{3}=3a^{3}(25a^{2}+60a+36)=3a^{3}(5a+6)^2\)