Ontbinden in factoren (2)

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

1. \(48a^{7}+120a^{6}+75a^{5}\)
2. \(-49x^{7}-14x^{6}-x^{5}\)
3. \(150q^{12}+120q^{8}+24q^{4}\)
4. \(-5y^{4}+320y^{2}\)
5. \(-216y^{4}+360y^{3}-150y^{2}\)
6. \(-16p^{6}-24p^{4}-9p^{2}\)
7. \(180x^{20}-245x^{4}\)
8. \(-24x^{6}+6x^{2}\)
9. \(-25q^{6}-70q^{5}-49q^{4}\)
10. \(96b^{13}-144b^{8}q+54b^{3}q^2\)
11. \(384a^{9}+96a^{7}p+6a^{5}p^2\)
12. \(180x^{4}-125x^{2}\)

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

Verbetersleutel

1. \(48a^{7}+120a^{6}+75a^{5}=3a^{5}(16a^{2}+40a+25)=3a^{5}(4a+5)^2\)
2. \(-49x^{7}-14x^{6}-x^{5}=-x^{5}(49x^{2}+14x+1)=-x^{5}(7x+1)^2\)
3. \(150q^{12}+120q^{8}+24q^{4}=6q^{4}(25q^{8}+20q^4+4)=6q^{4}(5q^4+2)^2\)
4. \(-5y^{4}+320y^{2}=-5y^{2}(y^2-64)=-5y^{2}(y+8)(y-8)\)
5. \(-216y^{4}+360y^{3}-150y^{2}=-6y^{2}(36y^{2}-60y+25)=-6y^{2}(6y-5)^2\)
6. \(-16p^{6}-24p^{4}-9p^{2}=-p^{2}(16p^{4}+24p^2+9)=-p^{2}(4p^2+3)^2\)
7. \(180x^{20}-245x^{4}=5x^{4}(36x^{16}-49)=5x^{4}(6x^8+7)(6x^8-7)\)
8. \(-24x^{6}+6x^{2}=-6x^{2}(4x^{4}-1)=-6x^{2}(2x^2+1)(2x^2-1)\)
9. \(-25q^{6}-70q^{5}-49q^{4}=-q^{4}(25q^{2}+70q+49)=-q^{4}(5q+7)^2\)
10. \(96b^{13}-144b^{8}q+54b^{3}q^2=6b^{3}(16b^{10}-24b^5q+9q^2)=6b^{3}(4b^5-3q)^2\)
11. \(384a^{9}+96a^{7}p+6a^{5}p^2=6a^{5}(64a^{4}+16a^2p+p^2)=6a^{5}(8a^2+p)^2\)
12. \(180x^{4}-125x^{2}=5x^{2}(36x^{2}-25)=5x^{2}(6x+5)(6x-5)\)