Ontbinden in factoren (2)

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

1. \(-108x^{10}-36x^{6}y-3x^{2}y^2\)
2. \(-2b^{5}+8b^{3}\)
3. \(80p^{9}-280p^{6}q+245p^{3}q^2\)
4. \(-54b^{8}-144b^{6}p-96b^{4}p^2\)
5. \(18y^{5}-98y^{3}\)
6. \(-3b^{5}+6b^{4}-3b^{3}\)
7. \(2x^{7}-8x^{5}\)
8. \(-2s^{4}+20s^{3}-50s^{2}\)
9. \(72p^{9}+24p^{7}q+2p^{5}q^2\)
10. \(32q^{4}-50q^{2}\)
11. \(24x^{11}-294x^{5}\)
12. \(-64b^{4}-112b^{3}-49b^{2}\)

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

Verbetersleutel

1. \(-108x^{10}-36x^{6}y-3x^{2}y^2=-3x^{2}(36x^{8}+12x^4y+y^2)=-3x^{2}(6x^4+y)^2\)
2. \(-2b^{5}+8b^{3}=-2b^{3}(b^2-4)=-2b^{3}(b-2)(b+2)\)
3. \(80p^{9}-280p^{6}q+245p^{3}q^2=5p^{3}(16p^{6}-56p^3q+49q^2)=5p^{3}(4p^3-7q)^2\)
4. \(-54b^{8}-144b^{6}p-96b^{4}p^2=-6b^{4}(9b^{4}+24b^2p+16p^2)=-6b^{4}(3b^2+4p)^2\)
5. \(18y^{5}-98y^{3}=2y^{3}(9y^{2}-49)=2y^{3}(3y+7)(3y-7)\)
6. \(-3b^{5}+6b^{4}-3b^{3}=-3b^{3}(b^2-2b+1)=-3b^{3}(b-1)^2\)
7. \(2x^{7}-8x^{5}=2x^{5}(x^2-4)=2x^{5}(x-2)(x+2)\)
8. \(-2s^{4}+20s^{3}-50s^{2}=-2s^{2}(s^2-10s+25)=-2s^{2}(s-5)^2\)
9. \(72p^{9}+24p^{7}q+2p^{5}q^2=2p^{5}(36p^{4}+12p^2q+q^2)=2p^{5}(6p^2+q)^2\)
10. \(32q^{4}-50q^{2}=2q^{2}(16q^{2}-25)=2q^{2}(4q+5)(4q-5)\)
11. \(24x^{11}-294x^{5}=6x^{5}(4x^{6}-49)=6x^{5}(2x^3+7)(2x^3-7)\)
12. \(-64b^{4}-112b^{3}-49b^{2}=-b^{2}(64b^{2}+112b+49)=-b^{2}(8b+7)^2\)