Ontbinden in factoren (2)

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

1. \(-27q^{10}+75q^{2}\)
2. \(-64y^{4}-112y^{3}-49y^{2}\)
3. \(-96a^{7}-144a^{5}p-54a^{3}p^2\)
4. \(-32s^{7}+18s^{5}\)
5. \(180b^{6}-245b^{4}\)
6. \(3y^{6}-48y^{4}\)
7. \(-5s^{6}+20s^{5}-20s^{4}\)
8. \(-6s^{4}+6s^{2}\)
9. \(294a^{10}-252a^{7}x+54a^{4}x^2\)
10. \(25b^{7}-b^{5}\)
11. \(245p^{7}-420p^{5}s+180p^{3}s^2\)
12. \(-5p^{6}+60p^{5}-180p^{4}\)

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

Verbetersleutel

1. \(-27q^{10}+75q^{2}=-3q^{2}(9q^{8}-25)=-3q^{2}(3q^4+5)(3q^4-5)\)
2. \(-64y^{4}-112y^{3}-49y^{2}=-y^{2}(64y^{2}+112y+49)=-y^{2}(8y+7)^2\)
3. \(-96a^{7}-144a^{5}p-54a^{3}p^2=-6a^{3}(16a^{4}+24a^2p+9p^2)=-6a^{3}(4a^2+3p)^2\)
4. \(-32s^{7}+18s^{5}=-2s^{5}(16s^{2}-9)=-2s^{5}(4s+3)(4s-3)\)
5. \(180b^{6}-245b^{4}=5b^{4}(36b^{2}-49)=5b^{4}(6b+7)(6b-7)\)
6. \(3y^{6}-48y^{4}=3y^{4}(y^2-16)=3y^{4}(y+4)(y-4)\)
7. \(-5s^{6}+20s^{5}-20s^{4}=-5s^{4}(s^2-4s+4)=-5s^{4}(s-2)^2\)
8. \(-6s^{4}+6s^{2}=-6s^{2}(s^2-1)=-6s^{2}(s-1)(s+1)\)
9. \(294a^{10}-252a^{7}x+54a^{4}x^2=6a^{4}(49a^{6}-42a^3x+9x^2)=6a^{4}(7a^3-3x)^2\)
10. \(25b^{7}-b^{5}=b^{5}(25b^{2}-1)=b^{5}(5b+1)(5b-1)\)
11. \(245p^{7}-420p^{5}s+180p^{3}s^2=5p^{3}(49p^{4}-84p^2s+36s^2)=5p^{3}(7p^2-6s)^2\)
12. \(-5p^{6}+60p^{5}-180p^{4}=-5p^{4}(p^2-12p+36)=-5p^{4}(p-6)^2\)