Ontbinden in factoren (2)

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

1. \(-125x^{5}+5x^{3}\)
2. \(-4p^{15}+p^{3}\)
3. \(-8s^{6}+50s^{4}\)
4. \(-3x^{4}-12x^{3}-12x^{2}\)
5. \(49s^{8}+70s^{5}y+25s^{2}y^2\)
6. \(8p^{4}-18p^{2}\)
7. \(49b^{8}-84b^{5}+36b^{2}\)
8. \(8p^{14}+8p^{9}y+2p^{4}y^2\)
9. \(12b^{8}-27b^{2}\)
10. \(-20q^{11}-20q^{7}y-5q^{3}y^2\)
11. \(32s^{14}+48s^{9}+18s^{4}\)
12. \(-147x^{4}+378x^{3}-243x^{2}\)

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

Verbetersleutel

1. \(-125x^{5}+5x^{3}=-5x^{3}(25x^{2}-1)=-5x^{3}(5x+1)(5x-1)\)
2. \(-4p^{15}+p^{3}=-p^{3}(4p^{12}-1)=-p^{3}(2p^6+1)(2p^6-1)\)
3. \(-8s^{6}+50s^{4}=-2s^{4}(4s^{2}-25)=-2s^{4}(2s+5)(2s-5)\)
4. \(-3x^{4}-12x^{3}-12x^{2}=-3x^{2}(x^2+4x+4)=-3x^{2}(x+2)^2\)
5. \(49s^{8}+70s^{5}y+25s^{2}y^2=s^{2}(49s^{6}+70s^3y+25y^2)=s^{2}(7s^3+5y)^2\)
6. \(8p^{4}-18p^{2}=2p^{2}(4p^{2}-9)=2p^{2}(2p+3)(2p-3)\)
7. \(49b^{8}-84b^{5}+36b^{2}=b^{2}(49b^{6}-84b^3+36)=b^{2}(7b^3-6)^2\)
8. \(8p^{14}+8p^{9}y+2p^{4}y^2=2p^{4}(4p^{10}+4p^5y+y^2)=2p^{4}(2p^5+y)^2\)
9. \(12b^{8}-27b^{2}=3b^{2}(4b^{6}-9)=3b^{2}(2b^3+3)(2b^3-3)\)
10. \(-20q^{11}-20q^{7}y-5q^{3}y^2=-5q^{3}(4q^{8}+4q^4y+y^2)=-5q^{3}(2q^4+y)^2\)
11. \(32s^{14}+48s^{9}+18s^{4}=2s^{4}(16s^{10}+24s^5+9)=2s^{4}(4s^5+3)^2\)
12. \(-147x^{4}+378x^{3}-243x^{2}=-3x^{2}(49x^{2}-126x+81)=-3x^{2}(7x-9)^2\)