Ontbinden in factoren (2)

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

1. \(25b^{19}-b^{3}\)
2. \(2b^{4}-8b^{2}\)
3. \(-3x^{6}+108x^{4}\)
4. \(-20a^{10}+125a^{2}\)
5. \(-6a^{5}+6a^{3}\)
6. \(25a^{5}-70a^{4}+49a^{3}\)
7. \(-9x^{20}+16x^{4}\)
8. \(-216a^{13}+360a^{9}x-150a^{5}x^2\)
9. \(-32b^{11}+48b^{8}-18b^{5}\)
10. \(50p^{19}-8p^{5}\)
11. \(-32x^{5}+112x^{4}-98x^{3}\)
12. \(2x^{6}-50x^{4}\)

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

Verbetersleutel

1. \(25b^{19}-b^{3}=b^{3}(25b^{16}-1)=b^{3}(5b^8+1)(5b^8-1)\)
2. \(2b^{4}-8b^{2}=2b^{2}(b^2-4)=2b^{2}(b+2)(b-2)\)
3. \(-3x^{6}+108x^{4}=-3x^{4}(x^2-36)=-3x^{4}(x-6)(x+6)\)
4. \(-20a^{10}+125a^{2}=-5a^{2}(4a^{8}-25)=-5a^{2}(2a^4+5)(2a^4-5)\)
5. \(-6a^{5}+6a^{3}=-6a^{3}(a^2-1)=-6a^{3}(a-1)(a+1)\)
6. \(25a^{5}-70a^{4}+49a^{3}=a^{3}(25a^{2}-70a+49)=a^{3}(5a-7)^2\)
7. \(-9x^{20}+16x^{4}=-x^{4}(9x^{16}-16)=-x^{4}(3x^8+4)(3x^8-4)\)
8. \(-216a^{13}+360a^{9}x-150a^{5}x^2=-6a^{5}(36a^{8}-60a^4x+25x^2)=-6a^{5}(6a^4-5x)^2\)
9. \(-32b^{11}+48b^{8}-18b^{5}=-2b^{5}(16b^{6}-24b^3+9)=-2b^{5}(4b^3-3)^2\)
10. \(50p^{19}-8p^{5}=2p^{5}(25p^{14}-4)=2p^{5}(5p^7+2)(5p^7-2)\)
11. \(-32x^{5}+112x^{4}-98x^{3}=-2x^{3}(16x^{2}-56x+49)=-2x^{3}(4x-7)^2\)
12. \(2x^{6}-50x^{4}=2x^{4}(x^2-25)=2x^{4}(x+5)(x-5)\)