Ontbinden in factoren (2)

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

1. \(-36b^{4}-60b^{3}-25b^{2}\)
2. \(-5q^{7}+40q^{6}-80q^{5}\)
3. \(-75b^{9}+3b^{5}\)
4. \(a^{6}-64a^{4}\)
5. \(-25x^{5}-80x^{4}-64x^{3}\)
6. \(-3b^{7}+48b^{5}\)
7. \(-8p^{4}+18p^{2}\)
8. \(54s^{4}+144s^{3}+96s^{2}\)
9. \(-150a^{6}+216a^{4}\)
10. \(32y^{4}+80y^{3}+50y^{2}\)
11. \(-18p^{12}+8p^{2}\)
12. \(320p^{10}+80p^{6}s+5p^{2}s^2\)

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

Verbetersleutel

1. \(-36b^{4}-60b^{3}-25b^{2}=-b^{2}(36b^{2}+60b+25)=-b^{2}(6b+5)^2\)
2. \(-5q^{7}+40q^{6}-80q^{5}=-5q^{5}(q^2-8q+16)=-5q^{5}(q-4)^2\)
3. \(-75b^{9}+3b^{5}=-3b^{5}(25b^{4}-1)=-3b^{5}(5b^2+1)(5b^2-1)\)
4. \(a^{6}-64a^{4}=a^{4}(a^2-64)=a^{4}(a-8)(a+8)\)
5. \(-25x^{5}-80x^{4}-64x^{3}=-x^{3}(25x^{2}+80x+64)=-x^{3}(5x+8)^2\)
6. \(-3b^{7}+48b^{5}=-3b^{5}(b^2-16)=-3b^{5}(b-4)(b+4)\)
7. \(-8p^{4}+18p^{2}=-2p^{2}(4p^{2}-9)=-2p^{2}(2p+3)(2p-3)\)
8. \(54s^{4}+144s^{3}+96s^{2}=6s^{2}(9s^{2}+24s+16)=6s^{2}(3s+4)^2\)
9. \(-150a^{6}+216a^{4}=-6a^{4}(25a^{2}-36)=-6a^{4}(5a+6)(5a-6)\)
10. \(32y^{4}+80y^{3}+50y^{2}=2y^{2}(16y^{2}+40y+25)=2y^{2}(4y+5)^2\)
11. \(-18p^{12}+8p^{2}=-2p^{2}(9p^{10}-4)=-2p^{2}(3p^5+2)(3p^5-2)\)
12. \(320p^{10}+80p^{6}s+5p^{2}s^2=5p^{2}(64p^{8}+16p^4s+s^2)=5p^{2}(8p^4+s)^2\)