Ontbinden in factoren (2)

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

1. \(32x^{11}+48x^{7}+18x^{3}\)
2. \(8y^{15}-50y^{5}\)
3. \(75x^{7}+180x^{6}+108x^{5}\)
4. \(3q^{4}-48q^{2}\)
5. \(-245p^{11}-350p^{8}q-125p^{5}q^2\)
6. \(16p^{6}-56p^{4}+49p^{2}\)
7. \(147b^{4}+84b^{3}+12b^{2}\)
8. \(50a^{10}+40a^{7}y+8a^{4}y^2\)
9. \(2q^{7}-50q^{5}\)
10. \(80s^{4}-5s^{2}\)
11. \(192s^{8}-240s^{5}y+75s^{2}y^2\)
12. \(2b^{4}-18b^{2}\)

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

Verbetersleutel

1. \(32x^{11}+48x^{7}+18x^{3}=2x^{3}(16x^{8}+24x^4+9)=2x^{3}(4x^4+3)^2\)
2. \(8y^{15}-50y^{5}=2y^{5}(4y^{10}-25)=2y^{5}(2y^5+5)(2y^5-5)\)
3. \(75x^{7}+180x^{6}+108x^{5}=3x^{5}(25x^{2}+60x+36)=3x^{5}(5x+6)^2\)
4. \(3q^{4}-48q^{2}=3q^{2}(q^2-16)=3q^{2}(q-4)(q+4)\)
5. \(-245p^{11}-350p^{8}q-125p^{5}q^2=-5p^{5}(49p^{6}+70p^3q+25q^2)=-5p^{5}(7p^3+5q)^2\)
6. \(16p^{6}-56p^{4}+49p^{2}=p^{2}(16p^{4}-56p^2+49)=p^{2}(4p^2-7)^2\)
7. \(147b^{4}+84b^{3}+12b^{2}=3b^{2}(49b^{2}+28b+4)=3b^{2}(7b+2)^2\)
8. \(50a^{10}+40a^{7}y+8a^{4}y^2=2a^{4}(25a^{6}+20a^3y+4y^2)=2a^{4}(5a^3+2y)^2\)
9. \(2q^{7}-50q^{5}=2q^{5}(q^2-25)=2q^{5}(q+5)(q-5)\)
10. \(80s^{4}-5s^{2}=5s^{2}(16s^{2}-1)=5s^{2}(4s+1)(4s-1)\)
11. \(192s^{8}-240s^{5}y+75s^{2}y^2=3s^{2}(64s^{6}-80s^3y+25y^2)=3s^{2}(8s^3-5y)^2\)
12. \(2b^{4}-18b^{2}=2b^{2}(b^2-9)=2b^{2}(b+3)(b-3)\)