Ontbinden in factoren (2)

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

1. \(-150a^{13}+216a^{3}\)
2. \(80b^{4}+280b^{3}+245b^{2}\)
3. \(-5q^{5}+5q^{3}\)
4. \(-3q^{7}+24q^{6}-48q^{5}\)
5. \(-5p^{6}+80p^{5}-320p^{4}\)
6. \(48b^{15}-147b^{5}\)
7. \(5y^{4}+50y^{3}+125y^{2}\)
8. \(-128x^{5}-32x^{4}-2x^{3}\)
9. \(b^{5}-36b^{3}\)
10. \(75b^{14}-120b^{9}+48b^{4}\)
11. \(180q^{7}+60q^{5}+5q^{3}\)
12. \(48a^{11}+24a^{7}+3a^{3}\)

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

Verbetersleutel

1. \(-150a^{13}+216a^{3}=-6a^{3}(25a^{10}-36)=-6a^{3}(5a^5+6)(5a^5-6)\)
2. \(80b^{4}+280b^{3}+245b^{2}=5b^{2}(16b^{2}+56b+49)=5b^{2}(4b+7)^2\)
3. \(-5q^{5}+5q^{3}=-5q^{3}(q^2-1)=-5q^{3}(q+1)(q-1)\)
4. \(-3q^{7}+24q^{6}-48q^{5}=-3q^{5}(q^2-8q+16)=-3q^{5}(q-4)^2\)
5. \(-5p^{6}+80p^{5}-320p^{4}=-5p^{4}(p^2-16p+64)=-5p^{4}(p-8)^2\)
6. \(48b^{15}-147b^{5}=3b^{5}(16b^{10}-49)=3b^{5}(4b^5+7)(4b^5-7)\)
7. \(5y^{4}+50y^{3}+125y^{2}=5y^{2}(y^2+10y+25)=5y^{2}(y+5)^2\)
8. \(-128x^{5}-32x^{4}-2x^{3}=-2x^{3}(64x^{2}+16x+1)=-2x^{3}(8x+1)^2\)
9. \(b^{5}-36b^{3}=b^{3}(b^2-36)=b^{3}(b-6)(b+6)\)
10. \(75b^{14}-120b^{9}+48b^{4}=3b^{4}(25b^{10}-40b^5+16)=3b^{4}(5b^5-4)^2\)
11. \(180q^{7}+60q^{5}+5q^{3}=5q^{3}(36q^{4}+12q^2+1)=5q^{3}(6q^2+1)^2\)
12. \(48a^{11}+24a^{7}+3a^{3}=3a^{3}(16a^{8}+8a^4+1)=3a^{3}(4a^4+1)^2\)