Ontbinden in factoren (2)

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

1. \(-147x^{8}+84x^{6}y-12x^{4}y^2\)
2. \(-2x^{4}+8x^{2}\)
3. \(-36a^{7}+60a^{6}-25a^{5}\)
4. \(-q^{7}+16q^{5}\)
5. \(50p^{10}+20p^{7}s+2p^{4}s^2\)
6. \(18p^{5}-98p^{3}\)
7. \(-9b^{8}+12b^{5}-4b^{2}\)
8. \(-18p^{9}+24p^{6}y-8p^{3}y^2\)
9. \(-9a^{10}-12a^{6}-4a^{2}\)
10. \(245a^{10}+140a^{7}+20a^{4}\)
11. \(32a^{7}-112a^{5}p+98a^{3}p^2\)
12. \(75q^{12}-210q^{7}y+147q^{2}y^2\)

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

Verbetersleutel

1. \(-147x^{8}+84x^{6}y-12x^{4}y^2=-3x^{4}(49x^{4}-28x^2y+4y^2)=-3x^{4}(7x^2-2y)^2\)
2. \(-2x^{4}+8x^{2}=-2x^{2}(x^2-4)=-2x^{2}(x-2)(x+2)\)
3. \(-36a^{7}+60a^{6}-25a^{5}=-a^{5}(36a^{2}-60a+25)=-a^{5}(6a-5)^2\)
4. \(-q^{7}+16q^{5}=-q^{5}(q^2-16)=-q^{5}(q-4)(q+4)\)
5. \(50p^{10}+20p^{7}s+2p^{4}s^2=2p^{4}(25p^{6}+10p^3s+s^2)=2p^{4}(5p^3+s)^2\)
6. \(18p^{5}-98p^{3}=2p^{3}(9p^{2}-49)=2p^{3}(3p+7)(3p-7)\)
7. \(-9b^{8}+12b^{5}-4b^{2}=-b^{2}(9b^{6}-12b^3+4)=-b^{2}(3b^3-2)^2\)
8. \(-18p^{9}+24p^{6}y-8p^{3}y^2=-2p^{3}(9p^{6}-12p^3y+4y^2)=-2p^{3}(3p^3-2y)^2\)
9. \(-9a^{10}-12a^{6}-4a^{2}=-a^{2}(9a^{8}+12a^4+4)=-a^{2}(3a^4+2)^2\)
10. \(245a^{10}+140a^{7}+20a^{4}=5a^{4}(49a^{6}+28a^3+4)=5a^{4}(7a^3+2)^2\)
11. \(32a^{7}-112a^{5}p+98a^{3}p^2=2a^{3}(16a^{4}-56a^2p+49p^2)=2a^{3}(4a^2-7p)^2\)
12. \(75q^{12}-210q^{7}y+147q^{2}y^2=3q^{2}(25q^{10}-70q^5y+49y^2)=3q^{2}(5q^5-7y)^2\)