Ontbinden in factoren (2)

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

1. \(-216p^{5}+294p^{3}\)
2. \(12a^{12}-147a^{4}\)
3. \(-128b^{8}-96b^{5}-18b^{2}\)
4. \(-50y^{6}-180y^{5}-162y^{4}\)
5. \(72a^{11}+168a^{7}+98a^{3}\)
6. \(-16s^{4}-40s^{3}-25s^{2}\)
7. \(-128b^{10}-224b^{6}-98b^{2}\)
8. \(25y^{5}-90y^{4}+81y^{3}\)
9. \(25q^{6}+20q^{4}y+4q^{2}y^2\)
10. \(180q^{16}-245q^{2}\)
11. \(12y^{4}+108y^{3}+243y^{2}\)
12. \(-5a^{5}+90a^{4}-405a^{3}\)

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

Verbetersleutel

1. \(-216p^{5}+294p^{3}=-6p^{3}(36p^{2}-49)=-6p^{3}(6p+7)(6p-7)\)
2. \(12a^{12}-147a^{4}=3a^{4}(4a^{8}-49)=3a^{4}(2a^4+7)(2a^4-7)\)
3. \(-128b^{8}-96b^{5}-18b^{2}=-2b^{2}(64b^{6}+48b^3+9)=-2b^{2}(8b^3+3)^2\)
4. \(-50y^{6}-180y^{5}-162y^{4}=-2y^{4}(25y^{2}+90y+81)=-2y^{4}(5y+9)^2\)
5. \(72a^{11}+168a^{7}+98a^{3}=2a^{3}(36a^{8}+84a^4+49)=2a^{3}(6a^4+7)^2\)
6. \(-16s^{4}-40s^{3}-25s^{2}=-s^{2}(16s^{2}+40s+25)=-s^{2}(4s+5)^2\)
7. \(-128b^{10}-224b^{6}-98b^{2}=-2b^{2}(64b^{8}+112b^4+49)=-2b^{2}(8b^4+7)^2\)
8. \(25y^{5}-90y^{4}+81y^{3}=y^{3}(25y^{2}-90y+81)=y^{3}(5y-9)^2\)
9. \(25q^{6}+20q^{4}y+4q^{2}y^2=q^{2}(25q^{4}+20q^2y+4y^2)=q^{2}(5q^2+2y)^2\)
10. \(180q^{16}-245q^{2}=5q^{2}(36q^{14}-49)=5q^{2}(6q^7+7)(6q^7-7)\)
11. \(12y^{4}+108y^{3}+243y^{2}=3y^{2}(4y^{2}+36y+81)=3y^{2}(2y+9)^2\)
12. \(-5a^{5}+90a^{4}-405a^{3}=-5a^{3}(a^2-18a+81)=-5a^{3}(a-9)^2\)