Ontbinden in factoren (2)

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

1. \(-49y^{5}-28y^{4}-4y^{3}\)
2. \(5s^{6}-45s^{4}\)
3. \(-64a^{10}+80a^{7}p-25a^{4}p^2\)
4. \(36b^{12}-25b^{2}\)
5. \(-9y^{18}+49y^{2}\)
6. \(-x^{5}+36x^{3}\)
7. \(-96b^{6}+144b^{4}x-54b^{2}x^2\)
8. \(-s^{7}-12s^{6}-36s^{5}\)
9. \(-3x^{7}+54x^{6}-243x^{5}\)
10. \(25a^{6}-40a^{5}+16a^{4}\)
11. \(-32s^{4}+50s^{2}\)
12. \(128p^{15}+96p^{10}+18p^{5}\)

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

Verbetersleutel

1. \(-49y^{5}-28y^{4}-4y^{3}=-y^{3}(49y^{2}+28y+4)=-y^{3}(7y+2)^2\)
2. \(5s^{6}-45s^{4}=5s^{4}(s^2-9)=5s^{4}(s+3)(s-3)\)
3. \(-64a^{10}+80a^{7}p-25a^{4}p^2=-a^{4}(64a^{6}-80a^3p+25p^2)=-a^{4}(8a^3-5p)^2\)
4. \(36b^{12}-25b^{2}=b^{2}(36b^{10}-25)=b^{2}(6b^5+5)(6b^5-5)\)
5. \(-9y^{18}+49y^{2}=-y^{2}(9y^{16}-49)=-y^{2}(3y^8+7)(3y^8-7)\)
6. \(-x^{5}+36x^{3}=-x^{3}(x^2-36)=-x^{3}(x-6)(x+6)\)
7. \(-96b^{6}+144b^{4}x-54b^{2}x^2=-6b^{2}(16b^{4}-24b^2x+9x^2)=-6b^{2}(4b^2-3x)^2\)
8. \(-s^{7}-12s^{6}-36s^{5}=-s^{5}(s^2+12s+36)=-s^{5}(s+6)^2\)
9. \(-3x^{7}+54x^{6}-243x^{5}=-3x^{5}(x^2-18x+81)=-3x^{5}(x-9)^2\)
10. \(25a^{6}-40a^{5}+16a^{4}=a^{4}(25a^{2}-40a+16)=a^{4}(5a-4)^2\)
11. \(-32s^{4}+50s^{2}=-2s^{2}(16s^{2}-25)=-2s^{2}(4s+5)(4s-5)\)
12. \(128p^{15}+96p^{10}+18p^{5}=2p^{5}(64p^{10}+48p^5+9)=2p^{5}(8p^5+3)^2\)