Ontbinden in factoren (2)

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

1. \(384p^{6}-672p^{4}+294p^{2}\)
2. \(8y^{7}+8y^{5}+2y^{3}\)
3. \(-75q^{9}-90q^{6}-27q^{3}\)
4. \(216b^{17}-6b^{3}\)
5. \(45a^{9}-60a^{6}+20a^{3}\)
6. \(-8x^{5}+2x^{3}\)
7. \(-98b^{8}-84b^{5}-18b^{2}\)
8. \(2s^{5}+32s^{4}+128s^{3}\)
9. \(-b^{6}+b^{4}\)
10. \(-5a^{7}+245a^{5}\)
11. \(-150y^{11}+54y^{5}\)
12. \(24s^{4}+24s^{3}+6s^{2}\)

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

Verbetersleutel

1. \(384p^{6}-672p^{4}+294p^{2}=6p^{2}(64p^{4}-112p^2+49)=6p^{2}(8p^2-7)^2\)
2. \(8y^{7}+8y^{5}+2y^{3}=2y^{3}(4y^{4}+4y^2+1)=2y^{3}(2y^2+1)^2\)
3. \(-75q^{9}-90q^{6}-27q^{3}=-3q^{3}(25q^{6}+30q^3+9)=-3q^{3}(5q^3+3)^2\)
4. \(216b^{17}-6b^{3}=6b^{3}(36b^{14}-1)=6b^{3}(6b^7+1)(6b^7-1)\)
5. \(45a^{9}-60a^{6}+20a^{3}=5a^{3}(9a^{6}-12a^3+4)=5a^{3}(3a^3-2)^2\)
6. \(-8x^{5}+2x^{3}=-2x^{3}(4x^{2}-1)=-2x^{3}(2x+1)(2x-1)\)
7. \(-98b^{8}-84b^{5}-18b^{2}=-2b^{2}(49b^{6}+42b^3+9)=-2b^{2}(7b^3+3)^2\)
8. \(2s^{5}+32s^{4}+128s^{3}=2s^{3}(s^2+16s+64)=2s^{3}(s+8)^2\)
9. \(-b^{6}+b^{4}=-b^{4}(b^2-1)=-b^{4}(b-1)(b+1)\)
10. \(-5a^{7}+245a^{5}=-5a^{5}(a^2-49)=-5a^{5}(a-7)(a+7)\)
11. \(-150y^{11}+54y^{5}=-6y^{5}(25y^{6}-9)=-6y^{5}(5y^3+3)(5y^3-3)\)
12. \(24s^{4}+24s^{3}+6s^{2}=6s^{2}(4s^{2}+4s+1)=6s^{2}(2s+1)^2\)