Ontbinden in factoren (2)

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

1. \(-2y^{7}+128y^{5}\)
2. \(q^{7}-9q^{5}\)
3. \(5p^{6}-5p^{4}\)
4. \(-80a^{7}+5a^{5}\)
5. \(6y^{6}-150y^{4}\)
6. \(12a^{4}-27a^{2}\)
7. \(48q^{13}+120q^{9}y+75q^{5}y^2\)
8. \(-4p^{16}+25p^{4}\)
9. \(-320b^{5}+560b^{4}-245b^{3}\)
10. \(6x^{4}-96x^{2}\)
11. \(4x^{6}+4x^{5}+x^{4}\)
12. \(192b^{8}+48b^{6}+3b^{4}\)

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

Verbetersleutel

1. \(-2y^{7}+128y^{5}=-2y^{5}(y^2-64)=-2y^{5}(y+8)(y-8)\)
2. \(q^{7}-9q^{5}=q^{5}(q^2-9)=q^{5}(q+3)(q-3)\)
3. \(5p^{6}-5p^{4}=5p^{4}(p^2-1)=5p^{4}(p+1)(p-1)\)
4. \(-80a^{7}+5a^{5}=-5a^{5}(16a^{2}-1)=-5a^{5}(4a+1)(4a-1)\)
5. \(6y^{6}-150y^{4}=6y^{4}(y^2-25)=6y^{4}(y-5)(y+5)\)
6. \(12a^{4}-27a^{2}=3a^{2}(4a^{2}-9)=3a^{2}(2a+3)(2a-3)\)
7. \(48q^{13}+120q^{9}y+75q^{5}y^2=3q^{5}(16q^{8}+40q^4y+25y^2)=3q^{5}(4q^4+5y)^2\)
8. \(-4p^{16}+25p^{4}=-p^{4}(4p^{12}-25)=-p^{4}(2p^6+5)(2p^6-5)\)
9. \(-320b^{5}+560b^{4}-245b^{3}=-5b^{3}(64b^{2}-112b+49)=-5b^{3}(8b-7)^2\)
10. \(6x^{4}-96x^{2}=6x^{2}(x^2-16)=6x^{2}(x-4)(x+4)\)
11. \(4x^{6}+4x^{5}+x^{4}=x^{4}(4x^{2}+4x+1)=x^{4}(2x+1)^2\)
12. \(192b^{8}+48b^{6}+3b^{4}=3b^{4}(64b^{4}+16b^2+1)=3b^{4}(8b^2+1)^2\)