Ontbinden in factoren (2)

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

1. \(-75p^{5}+270p^{4}-243p^{3}\)
2. \(-27a^{13}-90a^{9}s-75a^{5}s^2\)
3. \(125a^{8}+150a^{6}y+45a^{4}y^2\)
4. \(-24a^{19}+54a^{5}\)
5. \(-384q^{4}-672q^{3}-294q^{2}\)
6. \(18y^{13}-24y^{8}+8y^{3}\)
7. \(b^{4}-16b^{2}\)
8. \(80x^{6}-125x^{4}\)
9. \(-6q^{7}+48q^{6}-96q^{5}\)
10. \(5p^{7}+40p^{6}+80p^{5}\)
11. \(-18x^{15}+2x^{3}\)
12. \(3b^{4}+48b^{3}+192b^{2}\)

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

Verbetersleutel

1. \(-75p^{5}+270p^{4}-243p^{3}=-3p^{3}(25p^{2}-90p+81)=-3p^{3}(5p-9)^2\)
2. \(-27a^{13}-90a^{9}s-75a^{5}s^2=-3a^{5}(9a^{8}+30a^4s+25s^2)=-3a^{5}(3a^4+5s)^2\)
3. \(125a^{8}+150a^{6}y+45a^{4}y^2=5a^{4}(25a^{4}+30a^2y+9y^2)=5a^{4}(5a^2+3y)^2\)
4. \(-24a^{19}+54a^{5}=-6a^{5}(4a^{14}-9)=-6a^{5}(2a^7+3)(2a^7-3)\)
5. \(-384q^{4}-672q^{3}-294q^{2}=-6q^{2}(64q^{2}+112q+49)=-6q^{2}(8q+7)^2\)
6. \(18y^{13}-24y^{8}+8y^{3}=2y^{3}(9y^{10}-12y^5+4)=2y^{3}(3y^5-2)^2\)
7. \(b^{4}-16b^{2}=b^{2}(b^2-16)=b^{2}(b-4)(b+4)\)
8. \(80x^{6}-125x^{4}=5x^{4}(16x^{2}-25)=5x^{4}(4x+5)(4x-5)\)
9. \(-6q^{7}+48q^{6}-96q^{5}=-6q^{5}(q^2-8q+16)=-6q^{5}(q-4)^2\)
10. \(5p^{7}+40p^{6}+80p^{5}=5p^{5}(p^2+8p+16)=5p^{5}(p+4)^2\)
11. \(-18x^{15}+2x^{3}=-2x^{3}(9x^{12}-1)=-2x^{3}(3x^6+1)(3x^6-1)\)
12. \(3b^{4}+48b^{3}+192b^{2}=3b^{2}(b^2+16b+64)=3b^{2}(b+8)^2\)