Ontbinden in factoren (2)

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

1. \(-20b^{21}+45b^{5}\)
2. \(-36s^{21}+49s^{5}\)
3. \(6a^{4}+48a^{3}+96a^{2}\)
4. \(-96x^{8}+144x^{5}-54x^{2}\)
5. \(45s^{7}+60s^{6}+20s^{5}\)
6. \(-5x^{5}+5x^{3}\)
7. \(48x^{9}-147x^{3}\)
8. \(-98y^{6}-140y^{5}-50y^{4}\)
9. \(72q^{7}+24q^{5}x+2q^{3}x^2\)
10. \(5s^{7}-245s^{5}\)
11. \(-18b^{12}-48b^{7}-32b^{2}\)
12. \(-5s^{4}+245s^{2}\)

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

Verbetersleutel

1. \(-20b^{21}+45b^{5}=-5b^{5}(4b^{16}-9)=-5b^{5}(2b^8+3)(2b^8-3)\)
2. \(-36s^{21}+49s^{5}=-s^{5}(36s^{16}-49)=-s^{5}(6s^8+7)(6s^8-7)\)
3. \(6a^{4}+48a^{3}+96a^{2}=6a^{2}(a^2+8a+16)=6a^{2}(a+4)^2\)
4. \(-96x^{8}+144x^{5}-54x^{2}=-6x^{2}(16x^{6}-24x^3+9)=-6x^{2}(4x^3-3)^2\)
5. \(45s^{7}+60s^{6}+20s^{5}=5s^{5}(9s^{2}+12s+4)=5s^{5}(3s+2)^2\)
6. \(-5x^{5}+5x^{3}=-5x^{3}(x^2-1)=-5x^{3}(x-1)(x+1)\)
7. \(48x^{9}-147x^{3}=3x^{3}(16x^{6}-49)=3x^{3}(4x^3+7)(4x^3-7)\)
8. \(-98y^{6}-140y^{5}-50y^{4}=-2y^{4}(49y^{2}+70y+25)=-2y^{4}(7y+5)^2\)
9. \(72q^{7}+24q^{5}x+2q^{3}x^2=2q^{3}(36q^{4}+12q^2x+x^2)=2q^{3}(6q^2+x)^2\)
10. \(5s^{7}-245s^{5}=5s^{5}(s^2-49)=5s^{5}(s-7)(s+7)\)
11. \(-18b^{12}-48b^{7}-32b^{2}=-2b^{2}(9b^{10}+24b^5+16)=-2b^{2}(3b^5+4)^2\)
12. \(-5s^{4}+245s^{2}=-5s^{2}(s^2-49)=-5s^{2}(s-7)(s+7)\)