Ontbinden in factoren (2)

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

1. \(320p^{8}+80p^{5}y+5p^{2}y^2\)
2. \(-54s^{13}+294s^{3}\)
3. \(25y^{6}-4y^{4}\)
4. \(180p^{4}-125p^{2}\)
5. \(50b^{7}+40b^{6}+8b^{5}\)
6. \(-s^{7}-12s^{6}-36s^{5}\)
7. \(-20a^{4}-20a^{3}-5a^{2}\)
8. \(-5y^{6}+245y^{4}\)
9. \(-36a^{15}-60a^{10}x-25a^{5}x^2\)
10. \(180b^{7}+60b^{5}+5b^{3}\)
11. \(8q^{8}+8q^{5}x+2q^{2}x^2\)
12. \(-12x^{11}-12x^{7}-3x^{3}\)

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

Verbetersleutel

1. \(320p^{8}+80p^{5}y+5p^{2}y^2=5p^{2}(64p^{6}+16p^3y+y^2)=5p^{2}(8p^3+y)^2\)
2. \(-54s^{13}+294s^{3}=-6s^{3}(9s^{10}-49)=-6s^{3}(3s^5+7)(3s^5-7)\)
3. \(25y^{6}-4y^{4}=y^{4}(25y^{2}-4)=y^{4}(5y+2)(5y-2)\)
4. \(180p^{4}-125p^{2}=5p^{2}(36p^{2}-25)=5p^{2}(6p+5)(6p-5)\)
5. \(50b^{7}+40b^{6}+8b^{5}=2b^{5}(25b^{2}+20b+4)=2b^{5}(5b+2)^2\)
6. \(-s^{7}-12s^{6}-36s^{5}=-s^{5}(s^2+12s+36)=-s^{5}(s+6)^2\)
7. \(-20a^{4}-20a^{3}-5a^{2}=-5a^{2}(4a^{2}+4a+1)=-5a^{2}(2a+1)^2\)
8. \(-5y^{6}+245y^{4}=-5y^{4}(y^2-49)=-5y^{4}(y+7)(y-7)\)
9. \(-36a^{15}-60a^{10}x-25a^{5}x^2=-a^{5}(36a^{10}+60a^5x+25x^2)=-a^{5}(6a^5+5x)^2\)
10. \(180b^{7}+60b^{5}+5b^{3}=5b^{3}(36b^{4}+12b^2+1)=5b^{3}(6b^2+1)^2\)
11. \(8q^{8}+8q^{5}x+2q^{2}x^2=2q^{2}(4q^{6}+4q^3x+x^2)=2q^{2}(2q^3+x)^2\)
12. \(-12x^{11}-12x^{7}-3x^{3}=-3x^{3}(4x^{8}+4x^4+1)=-3x^{3}(2x^4+1)^2\)