Ontbinden in factoren (2)

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

1. \(-45x^{12}+125x^{2}\)
2. \(-2a^{4}+50a^{2}\)
3. \(-9x^{7}+49x^{5}\)
4. \(-80p^{7}+45p^{3}\)
5. \(-54x^{5}+294x^{3}\)
6. \(32y^{5}-48y^{4}+18y^{3}\)
7. \(-125p^{14}-300p^{9}-180p^{4}\)
8. \(-320s^{4}+560s^{3}-245s^{2}\)
9. \(54b^{10}-72b^{6}y+24b^{2}y^2\)
10. \(8a^{5}+8a^{4}+2a^{3}\)
11. \(-96b^{7}-48b^{6}-6b^{5}\)
12. \(54y^{7}-294y^{5}\)

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

Verbetersleutel

1. \(-45x^{12}+125x^{2}=-5x^{2}(9x^{10}-25)=-5x^{2}(3x^5+5)(3x^5-5)\)
2. \(-2a^{4}+50a^{2}=-2a^{2}(a^2-25)=-2a^{2}(a-5)(a+5)\)
3. \(-9x^{7}+49x^{5}=-x^{5}(9x^{2}-49)=-x^{5}(3x+7)(3x-7)\)
4. \(-80p^{7}+45p^{3}=-5p^{3}(16p^{4}-9)=-5p^{3}(4p^2+3)(4p^2-3)\)
5. \(-54x^{5}+294x^{3}=-6x^{3}(9x^{2}-49)=-6x^{3}(3x+7)(3x-7)\)
6. \(32y^{5}-48y^{4}+18y^{3}=2y^{3}(16y^{2}-24y+9)=2y^{3}(4y-3)^2\)
7. \(-125p^{14}-300p^{9}-180p^{4}=-5p^{4}(25p^{10}+60p^5+36)=-5p^{4}(5p^5+6)^2\)
8. \(-320s^{4}+560s^{3}-245s^{2}=-5s^{2}(64s^{2}-112s+49)=-5s^{2}(8s-7)^2\)
9. \(54b^{10}-72b^{6}y+24b^{2}y^2=6b^{2}(9b^{8}-12b^4y+4y^2)=6b^{2}(3b^4-2y)^2\)
10. \(8a^{5}+8a^{4}+2a^{3}=2a^{3}(4a^{2}+4a+1)=2a^{3}(2a+1)^2\)
11. \(-96b^{7}-48b^{6}-6b^{5}=-6b^{5}(16b^{2}+8b+1)=-6b^{5}(4b+1)^2\)
12. \(54y^{7}-294y^{5}=6y^{5}(9y^{2}-49)=6y^{5}(3y+7)(3y-7)\)