Ontbinden in factoren (2)

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

1. \(-27y^{5}+48y^{3}\)
2. \(-2s^{5}-8s^{4}-8s^{3}\)
3. \(180b^{20}-125b^{4}\)
4. \(-5s^{6}+80s^{4}\)
5. \(-320x^{6}+560x^{5}-245x^{4}\)
6. \(54a^{10}-150a^{4}\)
7. \(-36a^{6}+49a^{4}\)
8. \(2s^{7}-4s^{6}+2s^{5}\)
9. \(-75s^{7}+147s^{5}\)
10. \(64x^{4}+112x^{3}+49x^{2}\)
11. \(8q^{5}-2q^{3}\)
12. \(64p^{13}-112p^{9}x+49p^{5}x^2\)

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

Verbetersleutel

1. \(-27y^{5}+48y^{3}=-3y^{3}(9y^{2}-16)=-3y^{3}(3y+4)(3y-4)\)
2. \(-2s^{5}-8s^{4}-8s^{3}=-2s^{3}(s^2+4s+4)=-2s^{3}(s+2)^2\)
3. \(180b^{20}-125b^{4}=5b^{4}(36b^{16}-25)=5b^{4}(6b^8+5)(6b^8-5)\)
4. \(-5s^{6}+80s^{4}=-5s^{4}(s^2-16)=-5s^{4}(s-4)(s+4)\)
5. \(-320x^{6}+560x^{5}-245x^{4}=-5x^{4}(64x^{2}-112x+49)=-5x^{4}(8x-7)^2\)
6. \(54a^{10}-150a^{4}=6a^{4}(9a^{6}-25)=6a^{4}(3a^3+5)(3a^3-5)\)
7. \(-36a^{6}+49a^{4}=-a^{4}(36a^{2}-49)=-a^{4}(6a+7)(6a-7)\)
8. \(2s^{7}-4s^{6}+2s^{5}=2s^{5}(s^2-2s+1)=2s^{5}(s-1)^2\)
9. \(-75s^{7}+147s^{5}=-3s^{5}(25s^{2}-49)=-3s^{5}(5s+7)(5s-7)\)
10. \(64x^{4}+112x^{3}+49x^{2}=x^{2}(64x^{2}+112x+49)=x^{2}(8x+7)^2\)
11. \(8q^{5}-2q^{3}=2q^{3}(4q^{2}-1)=2q^{3}(2q+1)(2q-1)\)
12. \(64p^{13}-112p^{9}x+49p^{5}x^2=p^{5}(64p^{8}-112p^4x+49x^2)=p^{5}(8p^4-7x)^2\)