Ontbinden in factoren (2)

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

1. \(-80a^{18}+45a^{4}\)
2. \(-64x^{13}-16x^{9}y-x^{5}y^2\)
3. \(216q^{17}-150q^{5}\)
4. \(-49q^{13}+28q^{9}x-4q^{5}x^2\)
5. \(2a^{5}-12a^{4}+18a^{3}\)
6. \(-48p^{11}-24p^{7}y-3p^{3}y^2\)
7. \(72a^{13}+24a^{9}s+2a^{5}s^2\)
8. \(9p^{7}-12p^{6}+4p^{5}\)
9. \(216q^{5}-6q^{3}\)
10. \(18y^{9}+12y^{6}+2y^{3}\)
11. \(45p^{14}-150p^{9}+125p^{4}\)
12. \(3x^{5}-147x^{3}\)

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

Verbetersleutel

1. \(-80a^{18}+45a^{4}=-5a^{4}(16a^{14}-9)=-5a^{4}(4a^7+3)(4a^7-3)\)
2. \(-64x^{13}-16x^{9}y-x^{5}y^2=-x^{5}(64x^{8}+16x^4y+y^2)=-x^{5}(8x^4+y)^2\)
3. \(216q^{17}-150q^{5}=6q^{5}(36q^{12}-25)=6q^{5}(6q^6+5)(6q^6-5)\)
4. \(-49q^{13}+28q^{9}x-4q^{5}x^2=-q^{5}(49q^{8}-28q^4x+4x^2)=-q^{5}(7q^4-2x)^2\)
5. \(2a^{5}-12a^{4}+18a^{3}=2a^{3}(a^2-6a+9)=2a^{3}(a-3)^2\)
6. \(-48p^{11}-24p^{7}y-3p^{3}y^2=-3p^{3}(16p^{8}+8p^4y+y^2)=-3p^{3}(4p^4+y)^2\)
7. \(72a^{13}+24a^{9}s+2a^{5}s^2=2a^{5}(36a^{8}+12a^4s+s^2)=2a^{5}(6a^4+s)^2\)
8. \(9p^{7}-12p^{6}+4p^{5}=p^{5}(9p^{2}-12p+4)=p^{5}(3p-2)^2\)
9. \(216q^{5}-6q^{3}=6q^{3}(36q^{2}-1)=6q^{3}(6q+1)(6q-1)\)
10. \(18y^{9}+12y^{6}+2y^{3}=2y^{3}(9y^{6}+6y^3+1)=2y^{3}(3y^3+1)^2\)
11. \(45p^{14}-150p^{9}+125p^{4}=5p^{4}(9p^{10}-30p^5+25)=5p^{4}(3p^5-5)^2\)
12. \(3x^{5}-147x^{3}=3x^{3}(x^2-49)=3x^{3}(x-7)(x+7)\)