Ontbinden in factoren (2)

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

1. \(25b^{6}-b^{4}\)
2. \(-6b^{4}+384b^{2}\)
3. \(-75s^{11}+120s^{7}-48s^{3}\)
4. \(36y^{6}-60y^{4}+25y^{2}\)
5. \(-125s^{15}+200s^{10}-80s^{5}\)
6. \(36s^{15}+60s^{10}y+25s^{5}y^2\)
7. \(x^{7}-16x^{5}\)
8. \(-72p^{13}-24p^{8}q-2p^{3}q^2\)
9. \(36q^{9}+12q^{7}+q^{5}\)
10. \(24x^{10}-150x^{4}\)
11. \(108b^{7}-75b^{5}\)
12. \(64q^{9}+16q^{7}y+q^{5}y^2\)

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

Verbetersleutel

1. \(25b^{6}-b^{4}=b^{4}(25b^{2}-1)=b^{4}(5b+1)(5b-1)\)
2. \(-6b^{4}+384b^{2}=-6b^{2}(b^2-64)=-6b^{2}(b-8)(b+8)\)
3. \(-75s^{11}+120s^{7}-48s^{3}=-3s^{3}(25s^{8}-40s^4+16)=-3s^{3}(5s^4-4)^2\)
4. \(36y^{6}-60y^{4}+25y^{2}=y^{2}(36y^{4}-60y^2+25)=y^{2}(6y^2-5)^2\)
5. \(-125s^{15}+200s^{10}-80s^{5}=-5s^{5}(25s^{10}-40s^5+16)=-5s^{5}(5s^5-4)^2\)
6. \(36s^{15}+60s^{10}y+25s^{5}y^2=s^{5}(36s^{10}+60s^5y+25y^2)=s^{5}(6s^5+5y)^2\)
7. \(x^{7}-16x^{5}=x^{5}(x^2-16)=x^{5}(x+4)(x-4)\)
8. \(-72p^{13}-24p^{8}q-2p^{3}q^2=-2p^{3}(36p^{10}+12p^5q+q^2)=-2p^{3}(6p^5+q)^2\)
9. \(36q^{9}+12q^{7}+q^{5}=q^{5}(36q^{4}+12q^2+1)=q^{5}(6q^2+1)^2\)
10. \(24x^{10}-150x^{4}=6x^{4}(4x^{6}-25)=6x^{4}(2x^3+5)(2x^3-5)\)
11. \(108b^{7}-75b^{5}=3b^{5}(36b^{2}-25)=3b^{5}(6b+5)(6b-5)\)
12. \(64q^{9}+16q^{7}y+q^{5}y^2=q^{5}(64q^{4}+16q^2y+y^2)=q^{5}(8q^2+y)^2\)