Ontbinden in factoren (2)

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

1. \(b^{7}-64b^{5}\)
2. \(180x^{7}-125x^{5}\)
3. \(25b^{4}-16b^{2}\)
4. \(-192a^{7}-48a^{6}-3a^{5}\)
5. \(-3y^{7}+192y^{5}\)
6. \(80p^{11}-125p^{3}\)
7. \(-384b^{14}-96b^{9}-6b^{4}\)
8. \(5x^{6}-245x^{4}\)
9. \(-108q^{10}+180q^{7}s-75q^{4}s^2\)
10. \(-36a^{12}-60a^{7}b-25a^{2}b^2\)
11. \(12p^{10}+12p^{7}+3p^{4}\)
12. \(-80b^{4}-40b^{3}-5b^{2}\)

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

Verbetersleutel

1. \(b^{7}-64b^{5}=b^{5}(b^2-64)=b^{5}(b-8)(b+8)\)
2. \(180x^{7}-125x^{5}=5x^{5}(36x^{2}-25)=5x^{5}(6x+5)(6x-5)\)
3. \(25b^{4}-16b^{2}=b^{2}(25b^{2}-16)=b^{2}(5b+4)(5b-4)\)
4. \(-192a^{7}-48a^{6}-3a^{5}=-3a^{5}(64a^{2}+16a+1)=-3a^{5}(8a+1)^2\)
5. \(-3y^{7}+192y^{5}=-3y^{5}(y^2-64)=-3y^{5}(y-8)(y+8)\)
6. \(80p^{11}-125p^{3}=5p^{3}(16p^{8}-25)=5p^{3}(4p^4+5)(4p^4-5)\)
7. \(-384b^{14}-96b^{9}-6b^{4}=-6b^{4}(64b^{10}+16b^5+1)=-6b^{4}(8b^5+1)^2\)
8. \(5x^{6}-245x^{4}=5x^{4}(x^2-49)=5x^{4}(x+7)(x-7)\)
9. \(-108q^{10}+180q^{7}s-75q^{4}s^2=-3q^{4}(36q^{6}-60q^3s+25s^2)=-3q^{4}(6q^3-5s)^2\)
10. \(-36a^{12}-60a^{7}b-25a^{2}b^2=-a^{2}(36a^{10}+60a^5b+25b^2)=-a^{2}(6a^5+5b)^2\)
11. \(12p^{10}+12p^{7}+3p^{4}=3p^{4}(4p^{6}+4p^3+1)=3p^{4}(2p^3+1)^2\)
12. \(-80b^{4}-40b^{3}-5b^{2}=-5b^{2}(16b^{2}+8b+1)=-5b^{2}(4b+1)^2\)