Ontbinden in factoren (2)

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

1. \(49b^{13}+56b^{9}x+16b^{5}x^2\)
2. \(-3q^{7}+3q^{5}\)
3. \(75s^{5}-27s^{3}\)
4. \(18q^{7}-50q^{5}\)
5. \(9b^{7}+30b^{6}+25b^{5}\)
6. \(245x^{6}+420x^{5}+180x^{4}\)
7. \(245b^{13}+350b^{9}+125b^{5}\)
8. \(49y^{5}-84y^{4}+36y^{3}\)
9. \(-2y^{6}+8y^{4}\)
10. \(-9p^{6}+16p^{4}\)
11. \(-8x^{10}-8x^{6}-2x^{2}\)
12. \(-3q^{4}+36q^{3}-108q^{2}\)

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

Verbetersleutel

1. \(49b^{13}+56b^{9}x+16b^{5}x^2=b^{5}(49b^{8}+56b^4x+16x^2)=b^{5}(7b^4+4x)^2\)
2. \(-3q^{7}+3q^{5}=-3q^{5}(q^2-1)=-3q^{5}(q-1)(q+1)\)
3. \(75s^{5}-27s^{3}=3s^{3}(25s^{2}-9)=3s^{3}(5s+3)(5s-3)\)
4. \(18q^{7}-50q^{5}=2q^{5}(9q^{2}-25)=2q^{5}(3q+5)(3q-5)\)
5. \(9b^{7}+30b^{6}+25b^{5}=b^{5}(9b^{2}+30b+25)=b^{5}(3b+5)^2\)
6. \(245x^{6}+420x^{5}+180x^{4}=5x^{4}(49x^{2}+84x+36)=5x^{4}(7x+6)^2\)
7. \(245b^{13}+350b^{9}+125b^{5}=5b^{5}(49b^{8}+70b^4+25)=5b^{5}(7b^4+5)^2\)
8. \(49y^{5}-84y^{4}+36y^{3}=y^{3}(49y^{2}-84y+36)=y^{3}(7y-6)^2\)
9. \(-2y^{6}+8y^{4}=-2y^{4}(y^2-4)=-2y^{4}(y+2)(y-2)\)
10. \(-9p^{6}+16p^{4}=-p^{4}(9p^{2}-16)=-p^{4}(3p+4)(3p-4)\)
11. \(-8x^{10}-8x^{6}-2x^{2}=-2x^{2}(4x^{8}+4x^4+1)=-2x^{2}(2x^4+1)^2\)
12. \(-3q^{4}+36q^{3}-108q^{2}=-3q^{2}(q^2-12q+36)=-3q^{2}(q-6)^2\)