Ontbinden in factoren (2)

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

1. \(80b^{5}-125b^{3}\)
2. \(-3b^{4}+27b^{2}\)
3. \(-27x^{8}+90x^{5}-75x^{2}\)
4. \(-192b^{12}+336b^{7}-147b^{2}\)
5. \(-9a^{11}+30a^{7}s-25a^{3}s^2\)
6. \(20q^{4}-245q^{2}\)
7. \(-108q^{6}+180q^{5}-75q^{4}\)
8. \(54b^{8}+144b^{5}y+96b^{2}y^2\)
9. \(2a^{5}-72a^{3}\)
10. \(-27p^{6}-72p^{5}-48p^{4}\)
11. \(-16p^{11}-8p^{8}-p^{5}\)
12. \(-49b^{6}-14b^{4}p-b^{2}p^2\)

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

Verbetersleutel

1. \(80b^{5}-125b^{3}=5b^{3}(16b^{2}-25)=5b^{3}(4b+5)(4b-5)\)
2. \(-3b^{4}+27b^{2}=-3b^{2}(b^2-9)=-3b^{2}(b-3)(b+3)\)
3. \(-27x^{8}+90x^{5}-75x^{2}=-3x^{2}(9x^{6}-30x^3+25)=-3x^{2}(3x^3-5)^2\)
4. \(-192b^{12}+336b^{7}-147b^{2}=-3b^{2}(64b^{10}-112b^5+49)=-3b^{2}(8b^5-7)^2\)
5. \(-9a^{11}+30a^{7}s-25a^{3}s^2=-a^{3}(9a^{8}-30a^4s+25s^2)=-a^{3}(3a^4-5s)^2\)
6. \(20q^{4}-245q^{2}=5q^{2}(4q^{2}-49)=5q^{2}(2q+7)(2q-7)\)
7. \(-108q^{6}+180q^{5}-75q^{4}=-3q^{4}(36q^{2}-60q+25)=-3q^{4}(6q-5)^2\)
8. \(54b^{8}+144b^{5}y+96b^{2}y^2=6b^{2}(9b^{6}+24b^3y+16y^2)=6b^{2}(3b^3+4y)^2\)
9. \(2a^{5}-72a^{3}=2a^{3}(a^2-36)=2a^{3}(a+6)(a-6)\)
10. \(-27p^{6}-72p^{5}-48p^{4}=-3p^{4}(9p^{2}+24p+16)=-3p^{4}(3p+4)^2\)
11. \(-16p^{11}-8p^{8}-p^{5}=-p^{5}(16p^{6}+8p^3+1)=-p^{5}(4p^3+1)^2\)
12. \(-49b^{6}-14b^{4}p-b^{2}p^2=-b^{2}(49b^{4}+14b^2p+p^2)=-b^{2}(7b^2+p)^2\)