Ontbinden in factoren (2)

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

1. \(320a^{9}+400a^{7}y+125a^{5}y^2\)
2. \(-16y^{19}+49y^{3}\)
3. \(54b^{9}+36b^{7}p+6b^{5}p^2\)
4. \(-5s^{6}+125s^{4}\)
5. \(18p^{5}+84p^{4}+98p^{3}\)
6. \(-3x^{6}+18x^{5}-27x^{4}\)
7. \(3b^{4}-48b^{3}+192b^{2}\)
8. \(5q^{7}-5q^{5}\)
9. \(p^{7}-49p^{5}\)
10. \(-36x^{7}+25x^{3}\)
11. \(-x^{6}+10x^{5}-25x^{4}\)
12. \(108b^{10}-180b^{7}x+75b^{4}x^2\)

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

Verbetersleutel

1. \(320a^{9}+400a^{7}y+125a^{5}y^2=5a^{5}(64a^{4}+80a^2y+25y^2)=5a^{5}(8a^2+5y)^2\)
2. \(-16y^{19}+49y^{3}=-y^{3}(16y^{16}-49)=-y^{3}(4y^8+7)(4y^8-7)\)
3. \(54b^{9}+36b^{7}p+6b^{5}p^2=6b^{5}(9b^{4}+6b^2p+p^2)=6b^{5}(3b^2+p)^2\)
4. \(-5s^{6}+125s^{4}=-5s^{4}(s^2-25)=-5s^{4}(s-5)(s+5)\)
5. \(18p^{5}+84p^{4}+98p^{3}=2p^{3}(9p^{2}+42p+49)=2p^{3}(3p+7)^2\)
6. \(-3x^{6}+18x^{5}-27x^{4}=-3x^{4}(x^2-6x+9)=-3x^{4}(x-3)^2\)
7. \(3b^{4}-48b^{3}+192b^{2}=3b^{2}(b^2-16b+64)=3b^{2}(b-8)^2\)
8. \(5q^{7}-5q^{5}=5q^{5}(q^2-1)=5q^{5}(q-1)(q+1)\)
9. \(p^{7}-49p^{5}=p^{5}(p^2-49)=p^{5}(p+7)(p-7)\)
10. \(-36x^{7}+25x^{3}=-x^{3}(36x^{4}-25)=-x^{3}(6x^2+5)(6x^2-5)\)
11. \(-x^{6}+10x^{5}-25x^{4}=-x^{4}(x^2-10x+25)=-x^{4}(x-5)^2\)
12. \(108b^{10}-180b^{7}x+75b^{4}x^2=3b^{4}(36b^{6}-60b^3x+25x^2)=3b^{4}(6b^3-5x)^2\)