Ontbinden in factoren (2)

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

1. \(-54p^{5}+180p^{4}-150p^{3}\)
2. \(2a^{7}-8a^{5}\)
3. \(-2b^{5}+32b^{3}\)
4. \(-36q^{4}+60q^{3}-25q^{2}\)
5. \(-320x^{5}-80x^{4}-5x^{3}\)
6. \(9y^{13}-30y^{8}+25y^{3}\)
7. \(245b^{4}-420b^{3}+180b^{2}\)
8. \(-72s^{7}+120s^{6}-50s^{5}\)
9. \(-125p^{8}-300p^{5}-180p^{2}\)
10. \(-y^{4}+64y^{2}\)
11. \(2p^{4}-18p^{2}\)
12. \(8y^{15}-18y^{5}\)

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

Verbetersleutel

1. \(-54p^{5}+180p^{4}-150p^{3}=-6p^{3}(9p^{2}-30p+25)=-6p^{3}(3p-5)^2\)
2. \(2a^{7}-8a^{5}=2a^{5}(a^2-4)=2a^{5}(a-2)(a+2)\)
3. \(-2b^{5}+32b^{3}=-2b^{3}(b^2-16)=-2b^{3}(b-4)(b+4)\)
4. \(-36q^{4}+60q^{3}-25q^{2}=-q^{2}(36q^{2}-60q+25)=-q^{2}(6q-5)^2\)
5. \(-320x^{5}-80x^{4}-5x^{3}=-5x^{3}(64x^{2}+16x+1)=-5x^{3}(8x+1)^2\)
6. \(9y^{13}-30y^{8}+25y^{3}=y^{3}(9y^{10}-30y^5+25)=y^{3}(3y^5-5)^2\)
7. \(245b^{4}-420b^{3}+180b^{2}=5b^{2}(49b^{2}-84b+36)=5b^{2}(7b-6)^2\)
8. \(-72s^{7}+120s^{6}-50s^{5}=-2s^{5}(36s^{2}-60s+25)=-2s^{5}(6s-5)^2\)
9. \(-125p^{8}-300p^{5}-180p^{2}=-5p^{2}(25p^{6}+60p^3+36)=-5p^{2}(5p^3+6)^2\)
10. \(-y^{4}+64y^{2}=-y^{2}(y^2-64)=-y^{2}(y+8)(y-8)\)
11. \(2p^{4}-18p^{2}=2p^{2}(p^2-9)=2p^{2}(p+3)(p-3)\)
12. \(8y^{15}-18y^{5}=2y^{5}(4y^{10}-9)=2y^{5}(2y^5+3)(2y^5-3)\)