Ontbinden in factoren (2)

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

1. \(150a^{5}+360a^{4}+216a^{3}\)
2. \(150b^{6}+60b^{4}y+6b^{2}y^2\)
3. \(-147x^{7}+126x^{5}-27x^{3}\)
4. \(18x^{10}-32x^{4}\)
5. \(-6y^{6}+150y^{4}\)
6. \(-150a^{10}+120a^{6}x-24a^{2}x^2\)
7. \(-32y^{4}+50y^{2}\)
8. \(108x^{11}-147x^{3}\)
9. \(-24s^{14}+294s^{2}\)
10. \(2y^{4}-18y^{2}\)
11. \(-50y^{12}+140y^{8}-98y^{4}\)
12. \(p^{4}-10p^{3}+25p^{2}\)

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

Verbetersleutel

1. \(150a^{5}+360a^{4}+216a^{3}=6a^{3}(25a^{2}+60a+36)=6a^{3}(5a+6)^2\)
2. \(150b^{6}+60b^{4}y+6b^{2}y^2=6b^{2}(25b^{4}+10b^2y+y^2)=6b^{2}(5b^2+y)^2\)
3. \(-147x^{7}+126x^{5}-27x^{3}=-3x^{3}(49x^{4}-42x^2+9)=-3x^{3}(7x^2-3)^2\)
4. \(18x^{10}-32x^{4}=2x^{4}(9x^{6}-16)=2x^{4}(3x^3+4)(3x^3-4)\)
5. \(-6y^{6}+150y^{4}=-6y^{4}(y^2-25)=-6y^{4}(y-5)(y+5)\)
6. \(-150a^{10}+120a^{6}x-24a^{2}x^2=-6a^{2}(25a^{8}-20a^4x+4x^2)=-6a^{2}(5a^4-2x)^2\)
7. \(-32y^{4}+50y^{2}=-2y^{2}(16y^{2}-25)=-2y^{2}(4y+5)(4y-5)\)
8. \(108x^{11}-147x^{3}=3x^{3}(36x^{8}-49)=3x^{3}(6x^4+7)(6x^4-7)\)
9. \(-24s^{14}+294s^{2}=-6s^{2}(4s^{12}-49)=-6s^{2}(2s^6+7)(2s^6-7)\)
10. \(2y^{4}-18y^{2}=2y^{2}(y^2-9)=2y^{2}(y+3)(y-3)\)
11. \(-50y^{12}+140y^{8}-98y^{4}=-2y^{4}(25y^{8}-70y^4+49)=-2y^{4}(5y^4-7)^2\)
12. \(p^{4}-10p^{3}+25p^{2}=p^{2}(p^2-10p+25)=p^{2}(p-5)^2\)