Ontbinden in factoren (2)

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

1. \(32s^{7}-2s^{5}\)
2. \(5p^{5}-60p^{4}+180p^{3}\)
3. \(-108b^{10}+180b^{6}q-75b^{2}q^2\)
4. \(x^{4}-49x^{2}\)
5. \(-45p^{11}-60p^{7}-20p^{3}\)
6. \(-54a^{21}+150a^{5}\)
7. \(27y^{20}-147y^{4}\)
8. \(-98x^{12}-112x^{7}-32x^{2}\)
9. \(-245q^{11}-70q^{7}y-5q^{3}y^2\)
10. \(4a^{6}+4a^{5}+a^{4}\)
11. \(64q^{13}+16q^{8}x+q^{3}x^2\)
12. \(-192a^{6}-144a^{5}-27a^{4}\)

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

Verbetersleutel

1. \(32s^{7}-2s^{5}=2s^{5}(16s^{2}-1)=2s^{5}(4s+1)(4s-1)\)
2. \(5p^{5}-60p^{4}+180p^{3}=5p^{3}(p^2-12p+36)=5p^{3}(p-6)^2\)
3. \(-108b^{10}+180b^{6}q-75b^{2}q^2=-3b^{2}(36b^{8}-60b^4q+25q^2)=-3b^{2}(6b^4-5q)^2\)
4. \(x^{4}-49x^{2}=x^{2}(x^2-49)=x^{2}(x+7)(x-7)\)
5. \(-45p^{11}-60p^{7}-20p^{3}=-5p^{3}(9p^{8}+12p^4+4)=-5p^{3}(3p^4+2)^2\)
6. \(-54a^{21}+150a^{5}=-6a^{5}(9a^{16}-25)=-6a^{5}(3a^8+5)(3a^8-5)\)
7. \(27y^{20}-147y^{4}=3y^{4}(9y^{16}-49)=3y^{4}(3y^8+7)(3y^8-7)\)
8. \(-98x^{12}-112x^{7}-32x^{2}=-2x^{2}(49x^{10}+56x^5+16)=-2x^{2}(7x^5+4)^2\)
9. \(-245q^{11}-70q^{7}y-5q^{3}y^2=-5q^{3}(49q^{8}+14q^4y+y^2)=-5q^{3}(7q^4+y)^2\)
10. \(4a^{6}+4a^{5}+a^{4}=a^{4}(4a^{2}+4a+1)=a^{4}(2a+1)^2\)
11. \(64q^{13}+16q^{8}x+q^{3}x^2=q^{3}(64q^{10}+16q^5x+x^2)=q^{3}(8q^5+x)^2\)
12. \(-192a^{6}-144a^{5}-27a^{4}=-3a^{4}(64a^{2}+48a+9)=-3a^{4}(8a+3)^2\)