Ontbinden in factoren (2)

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

1. \(-3b^{6}+48b^{4}\)
2. \(36p^{9}+12p^{7}s+p^{5}s^2\)
3. \(2s^{7}+24s^{6}+72s^{5}\)
4. \(-48b^{12}-72b^{7}p-27b^{2}p^2\)
5. \(96y^{6}-6y^{4}\)
6. \(-a^{7}+49a^{5}\)
7. \(-147q^{6}-42q^{4}x-3q^{2}x^2\)
8. \(36s^{5}-s^{3}\)
9. \(s^{5}+6s^{4}+9s^{3}\)
10. \(320p^{8}+80p^{5}q+5p^{2}q^2\)
11. \(125a^{12}-200a^{7}+80a^{2}\)
12. \(-3b^{5}+12b^{3}\)

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

Verbetersleutel

1. \(-3b^{6}+48b^{4}=-3b^{4}(b^2-16)=-3b^{4}(b+4)(b-4)\)
2. \(36p^{9}+12p^{7}s+p^{5}s^2=p^{5}(36p^{4}+12p^2s+s^2)=p^{5}(6p^2+s)^2\)
3. \(2s^{7}+24s^{6}+72s^{5}=2s^{5}(s^2+12s+36)=2s^{5}(s+6)^2\)
4. \(-48b^{12}-72b^{7}p-27b^{2}p^2=-3b^{2}(16b^{10}+24b^5p+9p^2)=-3b^{2}(4b^5+3p)^2\)
5. \(96y^{6}-6y^{4}=6y^{4}(16y^{2}-1)=6y^{4}(4y+1)(4y-1)\)
6. \(-a^{7}+49a^{5}=-a^{5}(a^2-49)=-a^{5}(a+7)(a-7)\)
7. \(-147q^{6}-42q^{4}x-3q^{2}x^2=-3q^{2}(49q^{4}+14q^2x+x^2)=-3q^{2}(7q^2+x)^2\)
8. \(36s^{5}-s^{3}=s^{3}(36s^{2}-1)=s^{3}(6s+1)(6s-1)\)
9. \(s^{5}+6s^{4}+9s^{3}=s^{3}(s^2+6s+9)=s^{3}(s+3)^2\)
10. \(320p^{8}+80p^{5}q+5p^{2}q^2=5p^{2}(64p^{6}+16p^3q+q^2)=5p^{2}(8p^3+q)^2\)
11. \(125a^{12}-200a^{7}+80a^{2}=5a^{2}(25a^{10}-40a^5+16)=5a^{2}(5a^5-4)^2\)
12. \(-3b^{5}+12b^{3}=-3b^{3}(b^2-4)=-3b^{3}(b+2)(b-2)\)