Ontbinden in factoren (2)

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

1. \(80p^{15}-120p^{10}s+45p^{5}s^2\)
2. \(q^{6}+2q^{5}+q^{4}\)
3. \(-25y^{4}+y^{2}\)
4. \(-2a^{7}+24a^{6}-72a^{5}\)
5. \(-20x^{15}+125x^{3}\)
6. \(-147b^{6}+252b^{4}-108b^{2}\)
7. \(27b^{13}+72b^{9}s+48b^{5}s^2\)
8. \(27s^{14}-36s^{9}+12s^{4}\)
9. \(9p^{4}-16p^{2}\)
10. \(-20y^{7}-20y^{6}-5y^{5}\)
11. \(-25a^{9}+40a^{6}-16a^{3}\)
12. \(108y^{7}+36y^{6}+3y^{5}\)

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

Verbetersleutel

1. \(80p^{15}-120p^{10}s+45p^{5}s^2=5p^{5}(16p^{10}-24p^5s+9s^2)=5p^{5}(4p^5-3s)^2\)
2. \(q^{6}+2q^{5}+q^{4}=q^{4}(q^2+2q+1)=q^{4}(q+1)^2\)
3. \(-25y^{4}+y^{2}=-y^{2}(25y^{2}-1)=-y^{2}(5y+1)(5y-1)\)
4. \(-2a^{7}+24a^{6}-72a^{5}=-2a^{5}(a^2-12a+36)=-2a^{5}(a-6)^2\)
5. \(-20x^{15}+125x^{3}=-5x^{3}(4x^{12}-25)=-5x^{3}(2x^6+5)(2x^6-5)\)
6. \(-147b^{6}+252b^{4}-108b^{2}=-3b^{2}(49b^{4}-84b^2+36)=-3b^{2}(7b^2-6)^2\)
7. \(27b^{13}+72b^{9}s+48b^{5}s^2=3b^{5}(9b^{8}+24b^4s+16s^2)=3b^{5}(3b^4+4s)^2\)
8. \(27s^{14}-36s^{9}+12s^{4}=3s^{4}(9s^{10}-12s^5+4)=3s^{4}(3s^5-2)^2\)
9. \(9p^{4}-16p^{2}=p^{2}(9p^{2}-16)=p^{2}(3p+4)(3p-4)\)
10. \(-20y^{7}-20y^{6}-5y^{5}=-5y^{5}(4y^{2}+4y+1)=-5y^{5}(2y+1)^2\)
11. \(-25a^{9}+40a^{6}-16a^{3}=-a^{3}(25a^{6}-40a^3+16)=-a^{3}(5a^3-4)^2\)
12. \(108y^{7}+36y^{6}+3y^{5}=3y^{5}(36y^{2}+12y+1)=3y^{5}(6y+1)^2\)