Ontbinden in factoren (2)

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

1. \(-96b^{14}+54b^{2}\)
2. \(50b^{11}-40b^{8}y+8b^{5}y^2\)
3. \(-75p^{6}+210p^{5}-147p^{4}\)
4. \(216x^{10}-150x^{2}\)
5. \(-50a^{7}-80a^{6}-32a^{5}\)
6. \(-147q^{12}-168q^{7}s-48q^{2}s^2\)
7. \(-50b^{6}+18b^{4}\)
8. \(49s^{7}+14s^{5}y+s^{3}y^2\)
9. \(-y^{6}-16y^{5}-64y^{4}\)
10. \(-108p^{4}-252p^{3}-147p^{2}\)
11. \(b^{7}-64b^{5}\)
12. \(-48s^{20}+75s^{4}\)

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

Verbetersleutel

1. \(-96b^{14}+54b^{2}=-6b^{2}(16b^{12}-9)=-6b^{2}(4b^6+3)(4b^6-3)\)
2. \(50b^{11}-40b^{8}y+8b^{5}y^2=2b^{5}(25b^{6}-20b^3y+4y^2)=2b^{5}(5b^3-2y)^2\)
3. \(-75p^{6}+210p^{5}-147p^{4}=-3p^{4}(25p^{2}-70p+49)=-3p^{4}(5p-7)^2\)
4. \(216x^{10}-150x^{2}=6x^{2}(36x^{8}-25)=6x^{2}(6x^4+5)(6x^4-5)\)
5. \(-50a^{7}-80a^{6}-32a^{5}=-2a^{5}(25a^{2}+40a+16)=-2a^{5}(5a+4)^2\)
6. \(-147q^{12}-168q^{7}s-48q^{2}s^2=-3q^{2}(49q^{10}+56q^5s+16s^2)=-3q^{2}(7q^5+4s)^2\)
7. \(-50b^{6}+18b^{4}=-2b^{4}(25b^{2}-9)=-2b^{4}(5b+3)(5b-3)\)
8. \(49s^{7}+14s^{5}y+s^{3}y^2=s^{3}(49s^{4}+14s^2y+y^2)=s^{3}(7s^2+y)^2\)
9. \(-y^{6}-16y^{5}-64y^{4}=-y^{4}(y^2+16y+64)=-y^{4}(y+8)^2\)
10. \(-108p^{4}-252p^{3}-147p^{2}=-3p^{2}(36p^{2}+84p+49)=-3p^{2}(6p+7)^2\)
11. \(b^{7}-64b^{5}=b^{5}(b^2-64)=b^{5}(b+8)(b-8)\)
12. \(-48s^{20}+75s^{4}=-3s^{4}(16s^{16}-25)=-3s^{4}(4s^8+5)(4s^8-5)\)