Ontbinden in factoren (2)

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

1. \(18x^{4}+60x^{3}+50x^{2}\)
2. \(12y^{8}+12y^{5}+3y^{2}\)
3. \(-25x^{15}+40x^{10}-16x^{5}\)
4. \(-5p^{5}+70p^{4}-245p^{3}\)
5. \(80x^{4}-45x^{2}\)
6. \(-3y^{6}+192y^{4}\)
7. \(-54a^{14}-36a^{9}b-6a^{4}b^2\)
8. \(-24y^{15}-24y^{10}-6y^{5}\)
9. \(2x^{4}+20x^{3}+50x^{2}\)
10. \(36s^{15}+60s^{10}y+25s^{5}y^2\)
11. \(96a^{6}-54a^{2}\)
12. \(-24b^{9}-24b^{6}y-6b^{3}y^2\)

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

Verbetersleutel

1. \(18x^{4}+60x^{3}+50x^{2}=2x^{2}(9x^{2}+30x+25)=2x^{2}(3x+5)^2\)
2. \(12y^{8}+12y^{5}+3y^{2}=3y^{2}(4y^{6}+4y^3+1)=3y^{2}(2y^3+1)^2\)
3. \(-25x^{15}+40x^{10}-16x^{5}=-x^{5}(25x^{10}-40x^5+16)=-x^{5}(5x^5-4)^2\)
4. \(-5p^{5}+70p^{4}-245p^{3}=-5p^{3}(p^2-14p+49)=-5p^{3}(p-7)^2\)
5. \(80x^{4}-45x^{2}=5x^{2}(16x^{2}-9)=5x^{2}(4x+3)(4x-3)\)
6. \(-3y^{6}+192y^{4}=-3y^{4}(y^2-64)=-3y^{4}(y+8)(y-8)\)
7. \(-54a^{14}-36a^{9}b-6a^{4}b^2=-6a^{4}(9a^{10}+6a^5b+b^2)=-6a^{4}(3a^5+b)^2\)
8. \(-24y^{15}-24y^{10}-6y^{5}=-6y^{5}(4y^{10}+4y^5+1)=-6y^{5}(2y^5+1)^2\)
9. \(2x^{4}+20x^{3}+50x^{2}=2x^{2}(x^2+10x+25)=2x^{2}(x+5)^2\)
10. \(36s^{15}+60s^{10}y+25s^{5}y^2=s^{5}(36s^{10}+60s^5y+25y^2)=s^{5}(6s^5+5y)^2\)
11. \(96a^{6}-54a^{2}=6a^{2}(16a^{4}-9)=6a^{2}(4a^2+3)(4a^2-3)\)
12. \(-24b^{9}-24b^{6}y-6b^{3}y^2=-6b^{3}(4b^{6}+4b^3y+y^2)=-6b^{3}(2b^3+y)^2\)