Ontbinden in factoren (2)

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

1. \(2b^{4}-32b^{2}\)
2. \(-125s^{10}-300s^{6}x-180s^{2}x^2\)
3. \(98y^{6}+112y^{5}+32y^{4}\)
4. \(-75s^{15}-30s^{10}-3s^{5}\)
5. \(45p^{10}+30p^{7}+5p^{4}\)
6. \(-5x^{6}-10x^{5}-5x^{4}\)
7. \(b^{7}+8b^{6}+16b^{5}\)
8. \(54q^{6}-294q^{4}\)
9. \(8x^{9}-2x^{5}\)
10. \(3a^{5}-108a^{3}\)
11. \(-24s^{15}-24s^{10}x-6s^{5}x^2\)
12. \(16q^{7}-9q^{5}\)

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

Verbetersleutel

1. \(2b^{4}-32b^{2}=2b^{2}(b^2-16)=2b^{2}(b+4)(b-4)\)
2. \(-125s^{10}-300s^{6}x-180s^{2}x^2=-5s^{2}(25s^{8}+60s^4x+36x^2)=-5s^{2}(5s^4+6x)^2\)
3. \(98y^{6}+112y^{5}+32y^{4}=2y^{4}(49y^{2}+56y+16)=2y^{4}(7y+4)^2\)
4. \(-75s^{15}-30s^{10}-3s^{5}=-3s^{5}(25s^{10}+10s^5+1)=-3s^{5}(5s^5+1)^2\)
5. \(45p^{10}+30p^{7}+5p^{4}=5p^{4}(9p^{6}+6p^3+1)=5p^{4}(3p^3+1)^2\)
6. \(-5x^{6}-10x^{5}-5x^{4}=-5x^{4}(x^2+2x+1)=-5x^{4}(x+1)^2\)
7. \(b^{7}+8b^{6}+16b^{5}=b^{5}(b^2+8b+16)=b^{5}(b+4)^2\)
8. \(54q^{6}-294q^{4}=6q^{4}(9q^{2}-49)=6q^{4}(3q+7)(3q-7)\)
9. \(8x^{9}-2x^{5}=2x^{5}(4x^{4}-1)=2x^{5}(2x^2+1)(2x^2-1)\)
10. \(3a^{5}-108a^{3}=3a^{3}(a^2-36)=3a^{3}(a-6)(a+6)\)
11. \(-24s^{15}-24s^{10}x-6s^{5}x^2=-6s^{5}(4s^{10}+4s^5x+x^2)=-6s^{5}(2s^5+x)^2\)
12. \(16q^{7}-9q^{5}=q^{5}(16q^{2}-9)=q^{5}(4q+3)(4q-3)\)