Ontbinden in factoren (2)

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

1. \(5b^{7}-45b^{5}\)
2. \(-16a^{9}+56a^{7}q-49a^{5}q^2\)
3. \(64s^{9}-112s^{7}y+49s^{5}y^2\)
4. \(50q^{8}-98q^{2}\)
5. \(x^{7}-8x^{6}+16x^{5}\)
6. \(6p^{4}-6p^{2}\)
7. \(-54s^{6}+96s^{4}\)
8. \(-8p^{4}+50p^{2}\)
9. \(180q^{7}-125q^{5}\)
10. \(-b^{5}+64b^{3}\)
11. \(-48b^{7}+3b^{5}\)
12. \(-4x^{5}-28x^{4}-49x^{3}\)

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

Verbetersleutel

1. \(5b^{7}-45b^{5}=5b^{5}(b^2-9)=5b^{5}(b-3)(b+3)\)
2. \(-16a^{9}+56a^{7}q-49a^{5}q^2=-a^{5}(16a^{4}-56a^2q+49q^2)=-a^{5}(4a^2-7q)^2\)
3. \(64s^{9}-112s^{7}y+49s^{5}y^2=s^{5}(64s^{4}-112s^2y+49y^2)=s^{5}(8s^2-7y)^2\)
4. \(50q^{8}-98q^{2}=2q^{2}(25q^{6}-49)=2q^{2}(5q^3+7)(5q^3-7)\)
5. \(x^{7}-8x^{6}+16x^{5}=x^{5}(x^2-8x+16)=x^{5}(x-4)^2\)
6. \(6p^{4}-6p^{2}=6p^{2}(p^2-1)=6p^{2}(p-1)(p+1)\)
7. \(-54s^{6}+96s^{4}=-6s^{4}(9s^{2}-16)=-6s^{4}(3s+4)(3s-4)\)
8. \(-8p^{4}+50p^{2}=-2p^{2}(4p^{2}-25)=-2p^{2}(2p+5)(2p-5)\)
9. \(180q^{7}-125q^{5}=5q^{5}(36q^{2}-25)=5q^{5}(6q+5)(6q-5)\)
10. \(-b^{5}+64b^{3}=-b^{3}(b^2-64)=-b^{3}(b-8)(b+8)\)
11. \(-48b^{7}+3b^{5}=-3b^{5}(16b^{2}-1)=-3b^{5}(4b+1)(4b-1)\)
12. \(-4x^{5}-28x^{4}-49x^{3}=-x^{3}(4x^{2}+28x+49)=-x^{3}(2x+7)^2\)