Ontbinden in factoren (2)

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

1. \(49p^{10}-84p^{7}q+36p^{4}q^2\)
2. \(-25p^{19}+p^{3}\)
3. \(-54x^{13}+72x^{8}-24x^{3}\)
4. \(72b^{6}-50b^{2}\)
5. \(-36q^{4}-60q^{3}-25q^{2}\)
6. \(-s^{6}+9s^{4}\)
7. \(-320s^{13}-80s^{8}x-5s^{3}x^2\)
8. \(-125y^{9}+80y^{5}\)
9. \(20s^{10}+20s^{6}x+5s^{2}x^2\)
10. \(-216a^{4}+150a^{2}\)
11. \(-80b^{6}-200b^{5}-125b^{4}\)
12. \(50p^{4}-18p^{2}\)

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

Verbetersleutel

1. \(49p^{10}-84p^{7}q+36p^{4}q^2=p^{4}(49p^{6}-84p^3q+36q^2)=p^{4}(7p^3-6q)^2\)
2. \(-25p^{19}+p^{3}=-p^{3}(25p^{16}-1)=-p^{3}(5p^8+1)(5p^8-1)\)
3. \(-54x^{13}+72x^{8}-24x^{3}=-6x^{3}(9x^{10}-12x^5+4)=-6x^{3}(3x^5-2)^2\)
4. \(72b^{6}-50b^{2}=2b^{2}(36b^{4}-25)=2b^{2}(6b^2+5)(6b^2-5)\)
5. \(-36q^{4}-60q^{3}-25q^{2}=-q^{2}(36q^{2}+60q+25)=-q^{2}(6q+5)^2\)
6. \(-s^{6}+9s^{4}=-s^{4}(s^2-9)=-s^{4}(s+3)(s-3)\)
7. \(-320s^{13}-80s^{8}x-5s^{3}x^2=-5s^{3}(64s^{10}+16s^5x+x^2)=-5s^{3}(8s^5+x)^2\)
8. \(-125y^{9}+80y^{5}=-5y^{5}(25y^{4}-16)=-5y^{5}(5y^2+4)(5y^2-4)\)
9. \(20s^{10}+20s^{6}x+5s^{2}x^2=5s^{2}(4s^{8}+4s^4x+x^2)=5s^{2}(2s^4+x)^2\)
10. \(-216a^{4}+150a^{2}=-6a^{2}(36a^{2}-25)=-6a^{2}(6a+5)(6a-5)\)
11. \(-80b^{6}-200b^{5}-125b^{4}=-5b^{4}(16b^{2}+40b+25)=-5b^{4}(4b+5)^2\)
12. \(50p^{4}-18p^{2}=2p^{2}(25p^{2}-9)=2p^{2}(5p+3)(5p-3)\)