Ontbinden in factoren (2)

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

1. \(36y^{5}-y^{3}\)
2. \(24y^{21}-294y^{5}\)
3. \(245q^{12}+70q^{7}s+5q^{2}s^2\)
4. \(-49b^{15}-14b^{10}x-b^{5}x^2\)
5. \(-98y^{9}-84y^{7}-18y^{5}\)
6. \(5x^{4}+70x^{3}+245x^{2}\)
7. \(-2p^{7}+8p^{5}\)
8. \(-108p^{6}-36p^{4}x-3p^{2}x^2\)
9. \(147s^{12}+252s^{7}x+108s^{2}x^2\)
10. \(-18y^{12}+98y^{4}\)
11. \(-98a^{4}+168a^{3}-72a^{2}\)
12. \(-16x^{7}+24x^{6}-9x^{5}\)

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

Verbetersleutel

1. \(36y^{5}-y^{3}=y^{3}(36y^{2}-1)=y^{3}(6y+1)(6y-1)\)
2. \(24y^{21}-294y^{5}=6y^{5}(4y^{16}-49)=6y^{5}(2y^8+7)(2y^8-7)\)
3. \(245q^{12}+70q^{7}s+5q^{2}s^2=5q^{2}(49q^{10}+14q^5s+s^2)=5q^{2}(7q^5+s)^2\)
4. \(-49b^{15}-14b^{10}x-b^{5}x^2=-b^{5}(49b^{10}+14b^5x+x^2)=-b^{5}(7b^5+x)^2\)
5. \(-98y^{9}-84y^{7}-18y^{5}=-2y^{5}(49y^{4}+42y^2+9)=-2y^{5}(7y^2+3)^2\)
6. \(5x^{4}+70x^{3}+245x^{2}=5x^{2}(x^2+14x+49)=5x^{2}(x+7)^2\)
7. \(-2p^{7}+8p^{5}=-2p^{5}(p^2-4)=-2p^{5}(p+2)(p-2)\)
8. \(-108p^{6}-36p^{4}x-3p^{2}x^2=-3p^{2}(36p^{4}+12p^2x+x^2)=-3p^{2}(6p^2+x)^2\)
9. \(147s^{12}+252s^{7}x+108s^{2}x^2=3s^{2}(49s^{10}+84s^5x+36x^2)=3s^{2}(7s^5+6x)^2\)
10. \(-18y^{12}+98y^{4}=-2y^{4}(9y^{8}-49)=-2y^{4}(3y^4+7)(3y^4-7)\)
11. \(-98a^{4}+168a^{3}-72a^{2}=-2a^{2}(49a^{2}-84a+36)=-2a^{2}(7a-6)^2\)
12. \(-16x^{7}+24x^{6}-9x^{5}=-x^{5}(16x^{2}-24x+9)=-x^{5}(4x-3)^2\)