Ontbinden in factoren (2)

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

1. \(-24b^{6}-24b^{4}-6b^{2}\)
2. \(-20x^{17}+125x^{3}\)
3. \(49y^{7}+14y^{6}+y^{5}\)
4. \(128a^{6}+32a^{5}+2a^{4}\)
5. \(9s^{14}+24s^{9}+16s^{4}\)
6. \(-96p^{14}+144p^{9}x-54p^{4}x^2\)
7. \(2b^{6}+8b^{5}+8b^{4}\)
8. \(-108s^{6}+75s^{4}\)
9. \(125s^{10}-180s^{4}\)
10. \(294a^{11}+84a^{7}x+6a^{3}x^2\)
11. \(-6y^{4}-24y^{3}-24y^{2}\)
12. \(150p^{19}-216p^{5}\)

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

Verbetersleutel

1. \(-24b^{6}-24b^{4}-6b^{2}=-6b^{2}(4b^{4}+4b^2+1)=-6b^{2}(2b^2+1)^2\)
2. \(-20x^{17}+125x^{3}=-5x^{3}(4x^{14}-25)=-5x^{3}(2x^7+5)(2x^7-5)\)
3. \(49y^{7}+14y^{6}+y^{5}=y^{5}(49y^{2}+14y+1)=y^{5}(7y+1)^2\)
4. \(128a^{6}+32a^{5}+2a^{4}=2a^{4}(64a^{2}+16a+1)=2a^{4}(8a+1)^2\)
5. \(9s^{14}+24s^{9}+16s^{4}=s^{4}(9s^{10}+24s^5+16)=s^{4}(3s^5+4)^2\)
6. \(-96p^{14}+144p^{9}x-54p^{4}x^2=-6p^{4}(16p^{10}-24p^5x+9x^2)=-6p^{4}(4p^5-3x)^2\)
7. \(2b^{6}+8b^{5}+8b^{4}=2b^{4}(b^2+4b+4)=2b^{4}(b+2)^2\)
8. \(-108s^{6}+75s^{4}=-3s^{4}(36s^{2}-25)=-3s^{4}(6s+5)(6s-5)\)
9. \(125s^{10}-180s^{4}=5s^{4}(25s^{6}-36)=5s^{4}(5s^3+6)(5s^3-6)\)
10. \(294a^{11}+84a^{7}x+6a^{3}x^2=6a^{3}(49a^{8}+14a^4x+x^2)=6a^{3}(7a^4+x)^2\)
11. \(-6y^{4}-24y^{3}-24y^{2}=-6y^{2}(y^2+4y+4)=-6y^{2}(y+2)^2\)
12. \(150p^{19}-216p^{5}=6p^{5}(25p^{14}-36)=6p^{5}(5p^7+6)(5p^7-6)\)