Ontbinden in factoren (2)

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

1. \(-27x^{7}+3x^{5}\)
2. \(-12p^{7}+75p^{5}\)
3. \(-64b^{10}+112b^{7}p-49b^{4}p^2\)
4. \(-36q^{10}+49q^{2}\)
5. \(-2p^{4}+32p^{2}\)
6. \(-49p^{12}-70p^{7}-25p^{2}\)
7. \(-2p^{7}-28p^{6}-98p^{5}\)
8. \(384p^{8}+288p^{6}+54p^{4}\)
9. \(216s^{7}+504s^{5}y+294s^{3}y^2\)
10. \(-3a^{5}-48a^{4}-192a^{3}\)
11. \(-147a^{12}-252a^{7}y-108a^{2}y^2\)
12. \(-18p^{18}+50p^{2}\)

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

Verbetersleutel

1. \(-27x^{7}+3x^{5}=-3x^{5}(9x^{2}-1)=-3x^{5}(3x+1)(3x-1)\)
2. \(-12p^{7}+75p^{5}=-3p^{5}(4p^{2}-25)=-3p^{5}(2p+5)(2p-5)\)
3. \(-64b^{10}+112b^{7}p-49b^{4}p^2=-b^{4}(64b^{6}-112b^3p+49p^2)=-b^{4}(8b^3-7p)^2\)
4. \(-36q^{10}+49q^{2}=-q^{2}(36q^{8}-49)=-q^{2}(6q^4+7)(6q^4-7)\)
5. \(-2p^{4}+32p^{2}=-2p^{2}(p^2-16)=-2p^{2}(p-4)(p+4)\)
6. \(-49p^{12}-70p^{7}-25p^{2}=-p^{2}(49p^{10}+70p^5+25)=-p^{2}(7p^5+5)^2\)
7. \(-2p^{7}-28p^{6}-98p^{5}=-2p^{5}(p^2+14p+49)=-2p^{5}(p+7)^2\)
8. \(384p^{8}+288p^{6}+54p^{4}=6p^{4}(64p^{4}+48p^2+9)=6p^{4}(8p^2+3)^2\)
9. \(216s^{7}+504s^{5}y+294s^{3}y^2=6s^{3}(36s^{4}+84s^2y+49y^2)=6s^{3}(6s^2+7y)^2\)
10. \(-3a^{5}-48a^{4}-192a^{3}=-3a^{3}(a^2+16a+64)=-3a^{3}(a+8)^2\)
11. \(-147a^{12}-252a^{7}y-108a^{2}y^2=-3a^{2}(49a^{10}+84a^5y+36y^2)=-3a^{2}(7a^5+6y)^2\)
12. \(-18p^{18}+50p^{2}=-2p^{2}(9p^{16}-25)=-2p^{2}(3p^8+5)(3p^8-5)\)