Ontbinden in factoren (2)

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

1. \(-320p^{12}-80p^{8}-5p^{4}\)
2. \(-3x^{6}+36x^{5}-108x^{4}\)
3. \(49x^{12}+56x^{8}+16x^{4}\)
4. \(6y^{6}+24y^{5}+24y^{4}\)
5. \(20a^{12}-5a^{4}\)
6. \(128b^{10}-224b^{6}y+98b^{2}y^2\)
7. \(-72p^{7}-24p^{6}-2p^{5}\)
8. \(4a^{10}-a^{2}\)
9. \(-50s^{7}+2s^{5}\)
10. \(-180b^{15}+300b^{10}p-125b^{5}p^2\)
11. \(27a^{12}+18a^{7}b+3a^{2}b^2\)
12. \(-12x^{9}+147x^{5}\)

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

Verbetersleutel

1. \(-320p^{12}-80p^{8}-5p^{4}=-5p^{4}(64p^{8}+16p^4+1)=-5p^{4}(8p^4+1)^2\)
2. \(-3x^{6}+36x^{5}-108x^{4}=-3x^{4}(x^2-12x+36)=-3x^{4}(x-6)^2\)
3. \(49x^{12}+56x^{8}+16x^{4}=x^{4}(49x^{8}+56x^4+16)=x^{4}(7x^4+4)^2\)
4. \(6y^{6}+24y^{5}+24y^{4}=6y^{4}(y^2+4y+4)=6y^{4}(y+2)^2\)
5. \(20a^{12}-5a^{4}=5a^{4}(4a^{8}-1)=5a^{4}(2a^4+1)(2a^4-1)\)
6. \(128b^{10}-224b^{6}y+98b^{2}y^2=2b^{2}(64b^{8}-112b^4y+49y^2)=2b^{2}(8b^4-7y)^2\)
7. \(-72p^{7}-24p^{6}-2p^{5}=-2p^{5}(36p^{2}+12p+1)=-2p^{5}(6p+1)^2\)
8. \(4a^{10}-a^{2}=a^{2}(4a^{8}-1)=a^{2}(2a^4+1)(2a^4-1)\)
9. \(-50s^{7}+2s^{5}=-2s^{5}(25s^{2}-1)=-2s^{5}(5s+1)(5s-1)\)
10. \(-180b^{15}+300b^{10}p-125b^{5}p^2=-5b^{5}(36b^{10}-60b^5p+25p^2)=-5b^{5}(6b^5-5p)^2\)
11. \(27a^{12}+18a^{7}b+3a^{2}b^2=3a^{2}(9a^{10}+6a^5b+b^2)=3a^{2}(3a^5+b)^2\)
12. \(-12x^{9}+147x^{5}=-3x^{5}(4x^{4}-49)=-3x^{5}(2x^2+7)(2x^2-7)\)