Ontbinden in factoren (2)

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

1. \(25a^{6}-20a^{4}s+4a^{2}s^2\)
2. \(80q^{12}+120q^{7}x+45q^{2}x^2\)
3. \(2b^{6}-72b^{4}\)
4. \(45s^{6}+240s^{5}+320s^{4}\)
5. \(-8s^{5}+18s^{3}\)
6. \(2x^{4}-98x^{2}\)
7. \(5b^{5}-45b^{3}\)
8. \(-64p^{7}+112p^{6}-49p^{5}\)
9. \(-32s^{20}+50s^{4}\)
10. \(12a^{6}+12a^{5}+3a^{4}\)
11. \(-25y^{19}+4y^{5}\)
12. \(-5b^{6}+180b^{4}\)

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

Verbetersleutel

1. \(25a^{6}-20a^{4}s+4a^{2}s^2=a^{2}(25a^{4}-20a^2s+4s^2)=a^{2}(5a^2-2s)^2\)
2. \(80q^{12}+120q^{7}x+45q^{2}x^2=5q^{2}(16q^{10}+24q^5x+9x^2)=5q^{2}(4q^5+3x)^2\)
3. \(2b^{6}-72b^{4}=2b^{4}(b^2-36)=2b^{4}(b-6)(b+6)\)
4. \(45s^{6}+240s^{5}+320s^{4}=5s^{4}(9s^{2}+48s+64)=5s^{4}(3s+8)^2\)
5. \(-8s^{5}+18s^{3}=-2s^{3}(4s^{2}-9)=-2s^{3}(2s+3)(2s-3)\)
6. \(2x^{4}-98x^{2}=2x^{2}(x^2-49)=2x^{2}(x+7)(x-7)\)
7. \(5b^{5}-45b^{3}=5b^{3}(b^2-9)=5b^{3}(b-3)(b+3)\)
8. \(-64p^{7}+112p^{6}-49p^{5}=-p^{5}(64p^{2}-112p+49)=-p^{5}(8p-7)^2\)
9. \(-32s^{20}+50s^{4}=-2s^{4}(16s^{16}-25)=-2s^{4}(4s^8+5)(4s^8-5)\)
10. \(12a^{6}+12a^{5}+3a^{4}=3a^{4}(4a^{2}+4a+1)=3a^{4}(2a+1)^2\)
11. \(-25y^{19}+4y^{5}=-y^{5}(25y^{14}-4)=-y^{5}(5y^7+2)(5y^7-2)\)
12. \(-5b^{6}+180b^{4}=-5b^{4}(b^2-36)=-5b^{4}(b+6)(b-6)\)