Ontbinden in factoren (2)

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

1. \(-32y^{18}+50y^{4}\)
2. \(-5p^{7}+320p^{5}\)
3. \(-3p^{5}+12p^{3}\)
4. \(27p^{6}-48p^{4}\)
5. \(-49b^{12}-14b^{8}q-b^{4}q^2\)
6. \(45y^{7}+210y^{6}+245y^{5}\)
7. \(125q^{7}+100q^{5}x+20q^{3}x^2\)
8. \(-b^{4}+b^{2}\)
9. \(-6b^{4}+84b^{3}-294b^{2}\)
10. \(2x^{6}+28x^{5}+98x^{4}\)
11. \(-32q^{6}+112q^{5}-98q^{4}\)
12. \(98a^{6}+28a^{5}+2a^{4}\)

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

Verbetersleutel

1. \(-32y^{18}+50y^{4}=-2y^{4}(16y^{14}-25)=-2y^{4}(4y^7+5)(4y^7-5)\)
2. \(-5p^{7}+320p^{5}=-5p^{5}(p^2-64)=-5p^{5}(p+8)(p-8)\)
3. \(-3p^{5}+12p^{3}=-3p^{3}(p^2-4)=-3p^{3}(p-2)(p+2)\)
4. \(27p^{6}-48p^{4}=3p^{4}(9p^{2}-16)=3p^{4}(3p+4)(3p-4)\)
5. \(-49b^{12}-14b^{8}q-b^{4}q^2=-b^{4}(49b^{8}+14b^4q+q^2)=-b^{4}(7b^4+q)^2\)
6. \(45y^{7}+210y^{6}+245y^{5}=5y^{5}(9y^{2}+42y+49)=5y^{5}(3y+7)^2\)
7. \(125q^{7}+100q^{5}x+20q^{3}x^2=5q^{3}(25q^{4}+20q^2x+4x^2)=5q^{3}(5q^2+2x)^2\)
8. \(-b^{4}+b^{2}=-b^{2}(b^2-1)=-b^{2}(b+1)(b-1)\)
9. \(-6b^{4}+84b^{3}-294b^{2}=-6b^{2}(b^2-14b+49)=-6b^{2}(b-7)^2\)
10. \(2x^{6}+28x^{5}+98x^{4}=2x^{4}(x^2+14x+49)=2x^{4}(x+7)^2\)
11. \(-32q^{6}+112q^{5}-98q^{4}=-2q^{4}(16q^{2}-56q+49)=-2q^{4}(4q-7)^2\)
12. \(98a^{6}+28a^{5}+2a^{4}=2a^{4}(49a^{2}+14a+1)=2a^{4}(7a+1)^2\)