Ontbinden in factoren (2)

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

1. \(294s^{9}-252s^{7}+54s^{5}\)
2. \(8x^{5}-50x^{3}\)
3. \(216y^{5}-6y^{3}\)
4. \(96y^{5}-6y^{3}\)
5. \(96q^{6}-336q^{4}+294q^{2}\)
6. \(-72a^{9}+120a^{7}p-50a^{5}p^2\)
7. \(2a^{7}-32a^{5}\)
8. \(3q^{7}-24q^{6}+48q^{5}\)
9. \(-6y^{6}-36y^{5}-54y^{4}\)
10. \(45s^{7}-150s^{6}+125s^{5}\)
11. \(-108b^{13}-180b^{8}-75b^{3}\)
12. \(320q^{15}-400q^{10}x+125q^{5}x^2\)

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

Verbetersleutel

1. \(294s^{9}-252s^{7}+54s^{5}=6s^{5}(49s^{4}-42s^2+9)=6s^{5}(7s^2-3)^2\)
2. \(8x^{5}-50x^{3}=2x^{3}(4x^{2}-25)=2x^{3}(2x+5)(2x-5)\)
3. \(216y^{5}-6y^{3}=6y^{3}(36y^{2}-1)=6y^{3}(6y+1)(6y-1)\)
4. \(96y^{5}-6y^{3}=6y^{3}(16y^{2}-1)=6y^{3}(4y+1)(4y-1)\)
5. \(96q^{6}-336q^{4}+294q^{2}=6q^{2}(16q^{4}-56q^2+49)=6q^{2}(4q^2-7)^2\)
6. \(-72a^{9}+120a^{7}p-50a^{5}p^2=-2a^{5}(36a^{4}-60a^2p+25p^2)=-2a^{5}(6a^2-5p)^2\)
7. \(2a^{7}-32a^{5}=2a^{5}(a^2-16)=2a^{5}(a+4)(a-4)\)
8. \(3q^{7}-24q^{6}+48q^{5}=3q^{5}(q^2-8q+16)=3q^{5}(q-4)^2\)
9. \(-6y^{6}-36y^{5}-54y^{4}=-6y^{4}(y^2+6y+9)=-6y^{4}(y+3)^2\)
10. \(45s^{7}-150s^{6}+125s^{5}=5s^{5}(9s^{2}-30s+25)=5s^{5}(3s-5)^2\)
11. \(-108b^{13}-180b^{8}-75b^{3}=-3b^{3}(36b^{10}+60b^5+25)=-3b^{3}(6b^5+5)^2\)
12. \(320q^{15}-400q^{10}x+125q^{5}x^2=5q^{5}(64q^{10}-80q^5x+25x^2)=5q^{5}(8q^5-5x)^2\)