Ontbinden in factoren (2)

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

1. \(6y^{6}-384y^{4}\)
2. \(45y^{4}-80y^{2}\)
3. \(72a^{12}-120a^{7}s+50a^{2}s^2\)
4. \(24s^{7}+24s^{6}+6s^{5}\)
5. \(3q^{5}+42q^{4}+147q^{3}\)
6. \(125x^{19}-180x^{5}\)
7. \(16q^{18}-25q^{4}\)
8. \(96b^{9}-150b^{5}\)
9. \(96s^{6}-144s^{5}+54s^{4}\)
10. \(-125x^{7}+45x^{5}\)
11. \(49x^{8}-84x^{6}+36x^{4}\)
12. \(108s^{5}-147s^{3}\)

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

Verbetersleutel

1. \(6y^{6}-384y^{4}=6y^{4}(y^2-64)=6y^{4}(y-8)(y+8)\)
2. \(45y^{4}-80y^{2}=5y^{2}(9y^{2}-16)=5y^{2}(3y+4)(3y-4)\)
3. \(72a^{12}-120a^{7}s+50a^{2}s^2=2a^{2}(36a^{10}-60a^5s+25s^2)=2a^{2}(6a^5-5s)^2\)
4. \(24s^{7}+24s^{6}+6s^{5}=6s^{5}(4s^{2}+4s+1)=6s^{5}(2s+1)^2\)
5. \(3q^{5}+42q^{4}+147q^{3}=3q^{3}(q^2+14q+49)=3q^{3}(q+7)^2\)
6. \(125x^{19}-180x^{5}=5x^{5}(25x^{14}-36)=5x^{5}(5x^7+6)(5x^7-6)\)
7. \(16q^{18}-25q^{4}=q^{4}(16q^{14}-25)=q^{4}(4q^7+5)(4q^7-5)\)
8. \(96b^{9}-150b^{5}=6b^{5}(16b^{4}-25)=6b^{5}(4b^2+5)(4b^2-5)\)
9. \(96s^{6}-144s^{5}+54s^{4}=6s^{4}(16s^{2}-24s+9)=6s^{4}(4s-3)^2\)
10. \(-125x^{7}+45x^{5}=-5x^{5}(25x^{2}-9)=-5x^{5}(5x+3)(5x-3)\)
11. \(49x^{8}-84x^{6}+36x^{4}=x^{4}(49x^{4}-84x^2+36)=x^{4}(7x^2-6)^2\)
12. \(108s^{5}-147s^{3}=3s^{3}(36s^{2}-49)=3s^{3}(6s+7)(6s-7)\)