Ontbinden in factoren (2)

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

1. \(125s^{13}+300s^{8}+180s^{3}\)
2. \(20x^{13}+60x^{9}y+45x^{5}y^2\)
3. \(216b^{5}-294b^{3}\)
4. \(98b^{8}+56b^{6}+8b^{4}\)
5. \(-6y^{6}+96y^{4}\)
6. \(24p^{5}-150p^{3}\)
7. \(-20x^{5}-100x^{4}-125x^{3}\)
8. \(45p^{11}-150p^{8}x+125p^{5}x^2\)
9. \(128y^{5}-224y^{4}+98y^{3}\)
10. \(2y^{7}-50y^{5}\)
11. \(27s^{6}-144s^{5}+192s^{4}\)
12. \(-2b^{6}+24b^{5}-72b^{4}\)

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

Verbetersleutel

1. \(125s^{13}+300s^{8}+180s^{3}=5s^{3}(25s^{10}+60s^5+36)=5s^{3}(5s^5+6)^2\)
2. \(20x^{13}+60x^{9}y+45x^{5}y^2=5x^{5}(4x^{8}+12x^4y+9y^2)=5x^{5}(2x^4+3y)^2\)
3. \(216b^{5}-294b^{3}=6b^{3}(36b^{2}-49)=6b^{3}(6b+7)(6b-7)\)
4. \(98b^{8}+56b^{6}+8b^{4}=2b^{4}(49b^{4}+28b^2+4)=2b^{4}(7b^2+2)^2\)
5. \(-6y^{6}+96y^{4}=-6y^{4}(y^2-16)=-6y^{4}(y-4)(y+4)\)
6. \(24p^{5}-150p^{3}=6p^{3}(4p^{2}-25)=6p^{3}(2p+5)(2p-5)\)
7. \(-20x^{5}-100x^{4}-125x^{3}=-5x^{3}(4x^{2}+20x+25)=-5x^{3}(2x+5)^2\)
8. \(45p^{11}-150p^{8}x+125p^{5}x^2=5p^{5}(9p^{6}-30p^3x+25x^2)=5p^{5}(3p^3-5x)^2\)
9. \(128y^{5}-224y^{4}+98y^{3}=2y^{3}(64y^{2}-112y+49)=2y^{3}(8y-7)^2\)
10. \(2y^{7}-50y^{5}=2y^{5}(y^2-25)=2y^{5}(y+5)(y-5)\)
11. \(27s^{6}-144s^{5}+192s^{4}=3s^{4}(9s^{2}-48s+64)=3s^{4}(3s-8)^2\)
12. \(-2b^{6}+24b^{5}-72b^{4}=-2b^{4}(b^2-12b+36)=-2b^{4}(b-6)^2\)