Ontbinden in factoren (2)

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

1. \(12p^{13}+36p^{8}x+27p^{3}x^2\)
2. \(18s^{14}-32s^{4}\)
3. \(18s^{4}-98s^{2}\)
4. \(3q^{5}-108q^{3}\)
5. \(3x^{6}+6x^{5}+3x^{4}\)
6. \(-9p^{9}+30p^{7}x-25p^{5}x^2\)
7. \(9b^{11}+12b^{8}+4b^{5}\)
8. \(-y^{7}+25y^{5}\)
9. \(-64p^{8}-16p^{6}s-p^{4}s^2\)
10. \(72b^{6}-2b^{2}\)
11. \(a^{4}-4a^{2}\)
12. \(54x^{14}-6x^{2}\)

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

Verbetersleutel

1. \(12p^{13}+36p^{8}x+27p^{3}x^2=3p^{3}(4p^{10}+12p^5x+9x^2)=3p^{3}(2p^5+3x)^2\)
2. \(18s^{14}-32s^{4}=2s^{4}(9s^{10}-16)=2s^{4}(3s^5+4)(3s^5-4)\)
3. \(18s^{4}-98s^{2}=2s^{2}(9s^{2}-49)=2s^{2}(3s+7)(3s-7)\)
4. \(3q^{5}-108q^{3}=3q^{3}(q^2-36)=3q^{3}(q+6)(q-6)\)
5. \(3x^{6}+6x^{5}+3x^{4}=3x^{4}(x^2+2x+1)=3x^{4}(x+1)^2\)
6. \(-9p^{9}+30p^{7}x-25p^{5}x^2=-p^{5}(9p^{4}-30p^2x+25x^2)=-p^{5}(3p^2-5x)^2\)
7. \(9b^{11}+12b^{8}+4b^{5}=b^{5}(9b^{6}+12b^3+4)=b^{5}(3b^3+2)^2\)
8. \(-y^{7}+25y^{5}=-y^{5}(y^2-25)=-y^{5}(y+5)(y-5)\)
9. \(-64p^{8}-16p^{6}s-p^{4}s^2=-p^{4}(64p^{4}+16p^2s+s^2)=-p^{4}(8p^2+s)^2\)
10. \(72b^{6}-2b^{2}=2b^{2}(36b^{4}-1)=2b^{2}(6b^2+1)(6b^2-1)\)
11. \(a^{4}-4a^{2}=a^{2}(a^2-4)=a^{2}(a-2)(a+2)\)
12. \(54x^{14}-6x^{2}=6x^{2}(9x^{12}-1)=6x^{2}(3x^6+1)(3x^6-1)\)