Ontbinden in factoren (2)

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

1. \(18p^{6}-60p^{4}+50p^{2}\)
2. \(-36x^{15}+60x^{10}-25x^{5}\)
3. \(32b^{6}+80b^{4}+50b^{2}\)
4. \(12a^{7}-147a^{5}\)
5. \(48x^{7}-3x^{5}\)
6. \(8p^{11}+8p^{7}y+2p^{3}y^2\)
7. \(6a^{6}-60a^{5}+150a^{4}\)
8. \(49y^{11}-42y^{8}+9y^{5}\)
9. \(y^{6}-49y^{4}\)
10. \(25x^{6}-x^{4}\)
11. \(27p^{7}-36p^{5}+12p^{3}\)
12. \(-384a^{12}+672a^{8}-294a^{4}\)

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

Verbetersleutel

1. \(18p^{6}-60p^{4}+50p^{2}=2p^{2}(9p^{4}-30p^2+25)=2p^{2}(3p^2-5)^2\)
2. \(-36x^{15}+60x^{10}-25x^{5}=-x^{5}(36x^{10}-60x^5+25)=-x^{5}(6x^5-5)^2\)
3. \(32b^{6}+80b^{4}+50b^{2}=2b^{2}(16b^{4}+40b^2+25)=2b^{2}(4b^2+5)^2\)
4. \(12a^{7}-147a^{5}=3a^{5}(4a^{2}-49)=3a^{5}(2a+7)(2a-7)\)
5. \(48x^{7}-3x^{5}=3x^{5}(16x^{2}-1)=3x^{5}(4x+1)(4x-1)\)
6. \(8p^{11}+8p^{7}y+2p^{3}y^2=2p^{3}(4p^{8}+4p^4y+y^2)=2p^{3}(2p^4+y)^2\)
7. \(6a^{6}-60a^{5}+150a^{4}=6a^{4}(a^2-10a+25)=6a^{4}(a-5)^2\)
8. \(49y^{11}-42y^{8}+9y^{5}=y^{5}(49y^{6}-42y^3+9)=y^{5}(7y^3-3)^2\)
9. \(y^{6}-49y^{4}=y^{4}(y^2-49)=y^{4}(y-7)(y+7)\)
10. \(25x^{6}-x^{4}=x^{4}(25x^{2}-1)=x^{4}(5x+1)(5x-1)\)
11. \(27p^{7}-36p^{5}+12p^{3}=3p^{3}(9p^{4}-12p^2+4)=3p^{3}(3p^2-2)^2\)
12. \(-384a^{12}+672a^{8}-294a^{4}=-6a^{4}(64a^{8}-112a^4+49)=-6a^{4}(8a^4-7)^2\)