Ontbinden in factoren (2)

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

1. \(49b^{7}+56b^{5}p+16b^{3}p^2\)
2. \(80x^{6}-120x^{4}y+45x^{2}y^2\)
3. \(-48q^{16}+27q^{2}\)
4. \(64s^{9}+16s^{6}+s^{3}\)
5. \(-a^{6}+4a^{4}\)
6. \(49x^{5}+84x^{4}+36x^{3}\)
7. \(-32x^{21}+98x^{5}\)
8. \(80b^{11}+40b^{8}q+5b^{5}q^2\)
9. \(150q^{14}-294q^{4}\)
10. \(-6y^{5}-60y^{4}-150y^{3}\)
11. \(3q^{7}-192q^{5}\)
12. \(-4x^{10}-4x^{6}-x^{2}\)

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

Verbetersleutel

1. \(49b^{7}+56b^{5}p+16b^{3}p^2=b^{3}(49b^{4}+56b^2p+16p^2)=b^{3}(7b^2+4p)^2\)
2. \(80x^{6}-120x^{4}y+45x^{2}y^2=5x^{2}(16x^{4}-24x^2y+9y^2)=5x^{2}(4x^2-3y)^2\)
3. \(-48q^{16}+27q^{2}=-3q^{2}(16q^{14}-9)=-3q^{2}(4q^7+3)(4q^7-3)\)
4. \(64s^{9}+16s^{6}+s^{3}=s^{3}(64s^{6}+16s^3+1)=s^{3}(8s^3+1)^2\)
5. \(-a^{6}+4a^{4}=-a^{4}(a^2-4)=-a^{4}(a-2)(a+2)\)
6. \(49x^{5}+84x^{4}+36x^{3}=x^{3}(49x^{2}+84x+36)=x^{3}(7x+6)^2\)
7. \(-32x^{21}+98x^{5}=-2x^{5}(16x^{16}-49)=-2x^{5}(4x^8+7)(4x^8-7)\)
8. \(80b^{11}+40b^{8}q+5b^{5}q^2=5b^{5}(16b^{6}+8b^3q+q^2)=5b^{5}(4b^3+q)^2\)
9. \(150q^{14}-294q^{4}=6q^{4}(25q^{10}-49)=6q^{4}(5q^5+7)(5q^5-7)\)
10. \(-6y^{5}-60y^{4}-150y^{3}=-6y^{3}(y^2+10y+25)=-6y^{3}(y+5)^2\)
11. \(3q^{7}-192q^{5}=3q^{5}(q^2-64)=3q^{5}(q+8)(q-8)\)
12. \(-4x^{10}-4x^{6}-x^{2}=-x^{2}(4x^{8}+4x^4+1)=-x^{2}(2x^4+1)^2\)