Ontbinden in factoren (2)

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

1. \(54q^{4}-96q^{2}\)
2. \(-80q^{7}+245q^{5}\)
3. \(-36b^{10}+60b^{6}x-25b^{2}x^2\)
4. \(5x^{6}+30x^{5}+45x^{4}\)
5. \(150b^{7}+120b^{5}+24b^{3}\)
6. \(2a^{7}-72a^{5}\)
7. \(3b^{7}-36b^{6}+108b^{5}\)
8. \(16q^{7}+8q^{6}+q^{5}\)
9. \(a^{6}-4a^{5}+4a^{4}\)
10. \(27p^{7}-48p^{5}\)
11. \(-108q^{7}+75q^{5}\)
12. \(-45s^{5}+80s^{3}\)

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

Verbetersleutel

1. \(54q^{4}-96q^{2}=6q^{2}(9q^{2}-16)=6q^{2}(3q+4)(3q-4)\)
2. \(-80q^{7}+245q^{5}=-5q^{5}(16q^{2}-49)=-5q^{5}(4q+7)(4q-7)\)
3. \(-36b^{10}+60b^{6}x-25b^{2}x^2=-b^{2}(36b^{8}-60b^4x+25x^2)=-b^{2}(6b^4-5x)^2\)
4. \(5x^{6}+30x^{5}+45x^{4}=5x^{4}(x^2+6x+9)=5x^{4}(x+3)^2\)
5. \(150b^{7}+120b^{5}+24b^{3}=6b^{3}(25b^{4}+20b^2+4)=6b^{3}(5b^2+2)^2\)
6. \(2a^{7}-72a^{5}=2a^{5}(a^2-36)=2a^{5}(a-6)(a+6)\)
7. \(3b^{7}-36b^{6}+108b^{5}=3b^{5}(b^2-12b+36)=3b^{5}(b-6)^2\)
8. \(16q^{7}+8q^{6}+q^{5}=q^{5}(16q^{2}+8q+1)=q^{5}(4q+1)^2\)
9. \(a^{6}-4a^{5}+4a^{4}=a^{4}(a^2-4a+4)=a^{4}(a-2)^2\)
10. \(27p^{7}-48p^{5}=3p^{5}(9p^{2}-16)=3p^{5}(3p+4)(3p-4)\)
11. \(-108q^{7}+75q^{5}=-3q^{5}(36q^{2}-25)=-3q^{5}(6q+5)(6q-5)\)
12. \(-45s^{5}+80s^{3}=-5s^{3}(9s^{2}-16)=-5s^{3}(3s+4)(3s-4)\)