Ontbinden in factoren (2)

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

1. \(-a^{7}-18a^{6}-81a^{5}\)
2. \(320a^{8}+80a^{5}s+5a^{2}s^2\)
3. \(-9b^{4}+16b^{2}\)
4. \(p^{4}-16p^{2}\)
5. \(49q^{4}+14q^{3}+q^{2}\)
6. \(20x^{11}-245x^{3}\)
7. \(-150p^{10}+240p^{6}x-96p^{2}x^2\)
8. \(-20q^{7}-20q^{5}-5q^{3}\)
9. \(6a^{5}-216a^{3}\)
10. \(27s^{10}+72s^{6}+48s^{2}\)
11. \(32a^{8}-50a^{2}\)
12. \(20y^{4}+20y^{3}+5y^{2}\)

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

Verbetersleutel

1. \(-a^{7}-18a^{6}-81a^{5}=-a^{5}(a^2+18a+81)=-a^{5}(a+9)^2\)
2. \(320a^{8}+80a^{5}s+5a^{2}s^2=5a^{2}(64a^{6}+16a^3s+s^2)=5a^{2}(8a^3+s)^2\)
3. \(-9b^{4}+16b^{2}=-b^{2}(9b^{2}-16)=-b^{2}(3b+4)(3b-4)\)
4. \(p^{4}-16p^{2}=p^{2}(p^2-16)=p^{2}(p-4)(p+4)\)
5. \(49q^{4}+14q^{3}+q^{2}=q^{2}(49q^{2}+14q+1)=q^{2}(7q+1)^2\)
6. \(20x^{11}-245x^{3}=5x^{3}(4x^{8}-49)=5x^{3}(2x^4+7)(2x^4-7)\)
7. \(-150p^{10}+240p^{6}x-96p^{2}x^2=-6p^{2}(25p^{8}-40p^4x+16x^2)=-6p^{2}(5p^4-4x)^2\)
8. \(-20q^{7}-20q^{5}-5q^{3}=-5q^{3}(4q^{4}+4q^2+1)=-5q^{3}(2q^2+1)^2\)
9. \(6a^{5}-216a^{3}=6a^{3}(a^2-36)=6a^{3}(a-6)(a+6)\)
10. \(27s^{10}+72s^{6}+48s^{2}=3s^{2}(9s^{8}+24s^4+16)=3s^{2}(3s^4+4)^2\)
11. \(32a^{8}-50a^{2}=2a^{2}(16a^{6}-25)=2a^{2}(4a^3+5)(4a^3-5)\)
12. \(20y^{4}+20y^{3}+5y^{2}=5y^{2}(4y^{2}+4y+1)=5y^{2}(2y+1)^2\)