Ontbinden in factoren (2)

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

1. \(50s^{4}-80s^{3}+32s^{2}\)
2. \(-45x^{6}-30x^{5}-5x^{4}\)
3. \(-16a^{11}+56a^{8}x-49a^{5}x^2\)
4. \(-9p^{10}+30p^{6}-25p^{2}\)
5. \(-80a^{7}+5a^{5}\)
6. \(-45p^{7}+80p^{5}\)
7. \(192b^{13}+144b^{9}x+27b^{5}x^2\)
8. \(48a^{8}-168a^{5}q+147a^{2}q^2\)
9. \(16q^{14}-9q^{4}\)
10. \(108y^{6}+36y^{5}+3y^{4}\)
11. \(-12q^{6}+27q^{4}\)
12. \(2a^{7}-18a^{5}\)

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

Verbetersleutel

1. \(50s^{4}-80s^{3}+32s^{2}=2s^{2}(25s^{2}-40s+16)=2s^{2}(5s-4)^2\)
2. \(-45x^{6}-30x^{5}-5x^{4}=-5x^{4}(9x^{2}+6x+1)=-5x^{4}(3x+1)^2\)
3. \(-16a^{11}+56a^{8}x-49a^{5}x^2=-a^{5}(16a^{6}-56a^3x+49x^2)=-a^{5}(4a^3-7x)^2\)
4. \(-9p^{10}+30p^{6}-25p^{2}=-p^{2}(9p^{8}-30p^4+25)=-p^{2}(3p^4-5)^2\)
5. \(-80a^{7}+5a^{5}=-5a^{5}(16a^{2}-1)=-5a^{5}(4a+1)(4a-1)\)
6. \(-45p^{7}+80p^{5}=-5p^{5}(9p^{2}-16)=-5p^{5}(3p+4)(3p-4)\)
7. \(192b^{13}+144b^{9}x+27b^{5}x^2=3b^{5}(64b^{8}+48b^4x+9x^2)=3b^{5}(8b^4+3x)^2\)
8. \(48a^{8}-168a^{5}q+147a^{2}q^2=3a^{2}(16a^{6}-56a^3q+49q^2)=3a^{2}(4a^3-7q)^2\)
9. \(16q^{14}-9q^{4}=q^{4}(16q^{10}-9)=q^{4}(4q^5+3)(4q^5-3)\)
10. \(108y^{6}+36y^{5}+3y^{4}=3y^{4}(36y^{2}+12y+1)=3y^{4}(6y+1)^2\)
11. \(-12q^{6}+27q^{4}=-3q^{4}(4q^{2}-9)=-3q^{4}(2q+3)(2q-3)\)
12. \(2a^{7}-18a^{5}=2a^{5}(a^2-9)=2a^{5}(a+3)(a-3)\)