Ontbinden in factoren (2)

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

1. \(125b^{5}-5b^{3}\)
2. \(-3x^{4}+147x^{2}\)
3. \(245x^{10}-210x^{7}+45x^{4}\)
4. \(25q^{7}-49q^{3}\)
5. \(-2a^{7}+72a^{5}\)
6. \(-294b^{6}-84b^{5}-6b^{4}\)
7. \(320q^{12}+240q^{8}+45q^{4}\)
8. \(48p^{7}-168p^{5}s+147p^{3}s^2\)
9. \(108p^{7}+36p^{5}y+3p^{3}y^2\)
10. \(b^{5}-16b^{4}+64b^{3}\)
11. \(-20y^{4}+45y^{2}\)
12. \(125p^{6}-100p^{4}x+20p^{2}x^2\)

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

Verbetersleutel

1. \(125b^{5}-5b^{3}=5b^{3}(25b^{2}-1)=5b^{3}(5b+1)(5b-1)\)
2. \(-3x^{4}+147x^{2}=-3x^{2}(x^2-49)=-3x^{2}(x+7)(x-7)\)
3. \(245x^{10}-210x^{7}+45x^{4}=5x^{4}(49x^{6}-42x^3+9)=5x^{4}(7x^3-3)^2\)
4. \(25q^{7}-49q^{3}=q^{3}(25q^{4}-49)=q^{3}(5q^2+7)(5q^2-7)\)
5. \(-2a^{7}+72a^{5}=-2a^{5}(a^2-36)=-2a^{5}(a-6)(a+6)\)
6. \(-294b^{6}-84b^{5}-6b^{4}=-6b^{4}(49b^{2}+14b+1)=-6b^{4}(7b+1)^2\)
7. \(320q^{12}+240q^{8}+45q^{4}=5q^{4}(64q^{8}+48q^4+9)=5q^{4}(8q^4+3)^2\)
8. \(48p^{7}-168p^{5}s+147p^{3}s^2=3p^{3}(16p^{4}-56p^2s+49s^2)=3p^{3}(4p^2-7s)^2\)
9. \(108p^{7}+36p^{5}y+3p^{3}y^2=3p^{3}(36p^{4}+12p^2y+y^2)=3p^{3}(6p^2+y)^2\)
10. \(b^{5}-16b^{4}+64b^{3}=b^{3}(b^2-16b+64)=b^{3}(b-8)^2\)
11. \(-20y^{4}+45y^{2}=-5y^{2}(4y^{2}-9)=-5y^{2}(2y+3)(2y-3)\)
12. \(125p^{6}-100p^{4}x+20p^{2}x^2=5p^{2}(25p^{4}-20p^2x+4x^2)=5p^{2}(5p^2-2x)^2\)