Ontbinden in factoren (2)

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

1. \(-80p^{8}-200p^{6}x-125p^{4}x^2\)
2. \(12q^{7}-3q^{5}\)
3. \(-64p^{6}+80p^{5}-25p^{4}\)
4. \(-5y^{7}+5y^{5}\)
5. \(180a^{7}-5a^{5}\)
6. \(3p^{4}-75p^{2}\)
7. \(-45y^{9}-30y^{7}-5y^{5}\)
8. \(27p^{12}-3p^{2}\)
9. \(-a^{5}+16a^{3}\)
10. \(-320a^{10}-80a^{6}-5a^{2}\)
11. \(-x^{7}+9x^{5}\)
12. \(216s^{6}-150s^{4}\)

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

Verbetersleutel

1. \(-80p^{8}-200p^{6}x-125p^{4}x^2=-5p^{4}(16p^{4}+40p^2x+25x^2)=-5p^{4}(4p^2+5x)^2\)
2. \(12q^{7}-3q^{5}=3q^{5}(4q^{2}-1)=3q^{5}(2q+1)(2q-1)\)
3. \(-64p^{6}+80p^{5}-25p^{4}=-p^{4}(64p^{2}-80p+25)=-p^{4}(8p-5)^2\)
4. \(-5y^{7}+5y^{5}=-5y^{5}(y^2-1)=-5y^{5}(y+1)(y-1)\)
5. \(180a^{7}-5a^{5}=5a^{5}(36a^{2}-1)=5a^{5}(6a+1)(6a-1)\)
6. \(3p^{4}-75p^{2}=3p^{2}(p^2-25)=3p^{2}(p+5)(p-5)\)
7. \(-45y^{9}-30y^{7}-5y^{5}=-5y^{5}(9y^{4}+6y^2+1)=-5y^{5}(3y^2+1)^2\)
8. \(27p^{12}-3p^{2}=3p^{2}(9p^{10}-1)=3p^{2}(3p^5+1)(3p^5-1)\)
9. \(-a^{5}+16a^{3}=-a^{3}(a^2-16)=-a^{3}(a-4)(a+4)\)
10. \(-320a^{10}-80a^{6}-5a^{2}=-5a^{2}(64a^{8}+16a^4+1)=-5a^{2}(8a^4+1)^2\)
11. \(-x^{7}+9x^{5}=-x^{5}(x^2-9)=-x^{5}(x+3)(x-3)\)
12. \(216s^{6}-150s^{4}=6s^{4}(36s^{2}-25)=6s^{4}(6s+5)(6s-5)\)