Ontbinden in factoren (2)

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

1. \(-45p^{7}+125p^{5}\)
2. \(-6b^{6}+54b^{4}\)
3. \(-5a^{4}+320a^{2}\)
4. \(-45x^{9}+150x^{7}-125x^{5}\)
5. \(50a^{6}-2a^{4}\)
6. \(6s^{5}-384s^{3}\)
7. \(-5b^{5}+5b^{3}\)
8. \(-25b^{7}+9b^{5}\)
9. \(-64y^{7}-112y^{6}-49y^{5}\)
10. \(-16x^{6}+x^{4}\)
11. \(-98p^{10}+168p^{6}q-72p^{2}q^2\)
12. \(75a^{4}-147a^{2}\)

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

Verbetersleutel

1. \(-45p^{7}+125p^{5}=-5p^{5}(9p^{2}-25)=-5p^{5}(3p+5)(3p-5)\)
2. \(-6b^{6}+54b^{4}=-6b^{4}(b^2-9)=-6b^{4}(b+3)(b-3)\)
3. \(-5a^{4}+320a^{2}=-5a^{2}(a^2-64)=-5a^{2}(a+8)(a-8)\)
4. \(-45x^{9}+150x^{7}-125x^{5}=-5x^{5}(9x^{4}-30x^2+25)=-5x^{5}(3x^2-5)^2\)
5. \(50a^{6}-2a^{4}=2a^{4}(25a^{2}-1)=2a^{4}(5a+1)(5a-1)\)
6. \(6s^{5}-384s^{3}=6s^{3}(s^2-64)=6s^{3}(s-8)(s+8)\)
7. \(-5b^{5}+5b^{3}=-5b^{3}(b^2-1)=-5b^{3}(b+1)(b-1)\)
8. \(-25b^{7}+9b^{5}=-b^{5}(25b^{2}-9)=-b^{5}(5b+3)(5b-3)\)
9. \(-64y^{7}-112y^{6}-49y^{5}=-y^{5}(64y^{2}+112y+49)=-y^{5}(8y+7)^2\)
10. \(-16x^{6}+x^{4}=-x^{4}(16x^{2}-1)=-x^{4}(4x+1)(4x-1)\)
11. \(-98p^{10}+168p^{6}q-72p^{2}q^2=-2p^{2}(49p^{8}-84p^4q+36q^2)=-2p^{2}(7p^4-6q)^2\)
12. \(75a^{4}-147a^{2}=3a^{2}(25a^{2}-49)=3a^{2}(5a+7)(5a-7)\)