Ontbinden in factoren (2)

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

1. \(32y^{7}-2y^{5}\)
2. \(98b^{11}-84b^{8}x+18b^{5}x^2\)
3. \(2b^{6}-18b^{4}\)
4. \(180b^{13}-5b^{3}\)
5. \(-150x^{7}+6x^{5}\)
6. \(-6b^{7}+108b^{6}-486b^{5}\)
7. \(-5p^{4}+180p^{2}\)
8. \(-3a^{5}+3a^{3}\)
9. \(75q^{5}-108q^{3}\)
10. \(54x^{12}-72x^{7}+24x^{2}\)
11. \(-96s^{6}+54s^{4}\)
12. \(24x^{12}-6x^{2}\)

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

Verbetersleutel

1. \(32y^{7}-2y^{5}=2y^{5}(16y^{2}-1)=2y^{5}(4y+1)(4y-1)\)
2. \(98b^{11}-84b^{8}x+18b^{5}x^2=2b^{5}(49b^{6}-42b^3x+9x^2)=2b^{5}(7b^3-3x)^2\)
3. \(2b^{6}-18b^{4}=2b^{4}(b^2-9)=2b^{4}(b-3)(b+3)\)
4. \(180b^{13}-5b^{3}=5b^{3}(36b^{10}-1)=5b^{3}(6b^5+1)(6b^5-1)\)
5. \(-150x^{7}+6x^{5}=-6x^{5}(25x^{2}-1)=-6x^{5}(5x+1)(5x-1)\)
6. \(-6b^{7}+108b^{6}-486b^{5}=-6b^{5}(b^2-18b+81)=-6b^{5}(b-9)^2\)
7. \(-5p^{4}+180p^{2}=-5p^{2}(p^2-36)=-5p^{2}(p+6)(p-6)\)
8. \(-3a^{5}+3a^{3}=-3a^{3}(a^2-1)=-3a^{3}(a+1)(a-1)\)
9. \(75q^{5}-108q^{3}=3q^{3}(25q^{2}-36)=3q^{3}(5q+6)(5q-6)\)
10. \(54x^{12}-72x^{7}+24x^{2}=6x^{2}(9x^{10}-12x^5+4)=6x^{2}(3x^5-2)^2\)
11. \(-96s^{6}+54s^{4}=-6s^{4}(16s^{2}-9)=-6s^{4}(4s+3)(4s-3)\)
12. \(24x^{12}-6x^{2}=6x^{2}(4x^{10}-1)=6x^{2}(2x^5+1)(2x^5-1)\)