Ontbinden in factoren (2)

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

1. \(320a^{6}-560a^{5}+245a^{4}\)
2. \(36s^{6}-25s^{4}\)
3. \(2x^{4}-28x^{3}+98x^{2}\)
4. \(-64y^{7}+80y^{6}-25y^{5}\)
5. \(16y^{10}+24y^{7}+9y^{4}\)
6. \(108x^{11}-75x^{3}\)
7. \(108p^{7}-3p^{5}\)
8. \(-6a^{4}+54a^{2}\)
9. \(-3q^{5}-54q^{4}-243q^{3}\)
10. \(-216q^{17}+6q^{5}\)
11. \(3b^{7}-3b^{5}\)
12. \(18p^{5}-98p^{3}\)

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

Verbetersleutel

1. \(320a^{6}-560a^{5}+245a^{4}=5a^{4}(64a^{2}-112a+49)=5a^{4}(8a-7)^2\)
2. \(36s^{6}-25s^{4}=s^{4}(36s^{2}-25)=s^{4}(6s+5)(6s-5)\)
3. \(2x^{4}-28x^{3}+98x^{2}=2x^{2}(x^2-14x+49)=2x^{2}(x-7)^2\)
4. \(-64y^{7}+80y^{6}-25y^{5}=-y^{5}(64y^{2}-80y+25)=-y^{5}(8y-5)^2\)
5. \(16y^{10}+24y^{7}+9y^{4}=y^{4}(16y^{6}+24y^3+9)=y^{4}(4y^3+3)^2\)
6. \(108x^{11}-75x^{3}=3x^{3}(36x^{8}-25)=3x^{3}(6x^4+5)(6x^4-5)\)
7. \(108p^{7}-3p^{5}=3p^{5}(36p^{2}-1)=3p^{5}(6p+1)(6p-1)\)
8. \(-6a^{4}+54a^{2}=-6a^{2}(a^2-9)=-6a^{2}(a-3)(a+3)\)
9. \(-3q^{5}-54q^{4}-243q^{3}=-3q^{3}(q^2+18q+81)=-3q^{3}(q+9)^2\)
10. \(-216q^{17}+6q^{5}=-6q^{5}(36q^{12}-1)=-6q^{5}(6q^6+1)(6q^6-1)\)
11. \(3b^{7}-3b^{5}=3b^{5}(b^2-1)=3b^{5}(b+1)(b-1)\)
12. \(18p^{5}-98p^{3}=2p^{3}(9p^{2}-49)=2p^{3}(3p+7)(3p-7)\)