Ontbinden in factoren (2)

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

1. \(2p^{7}-18p^{5}\)
2. \(-216b^{4}-72b^{3}-6b^{2}\)
3. \(-9s^{12}+30s^{7}x-25s^{2}x^2\)
4. \(-5q^{5}+320q^{3}\)
5. \(-6q^{6}+96q^{4}\)
6. \(98a^{10}+168a^{6}b+72a^{2}b^2\)
7. \(-75q^{8}-30q^{6}-3q^{4}\)
8. \(-25x^{8}+40x^{5}-16x^{2}\)
9. \(-72y^{13}+98y^{5}\)
10. \(20b^{7}-5b^{5}\)
11. \(-3a^{4}-30a^{3}-75a^{2}\)
12. \(12y^{15}+12y^{10}+3y^{5}\)

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

Verbetersleutel

1. \(2p^{7}-18p^{5}=2p^{5}(p^2-9)=2p^{5}(p-3)(p+3)\)
2. \(-216b^{4}-72b^{3}-6b^{2}=-6b^{2}(36b^{2}+12b+1)=-6b^{2}(6b+1)^2\)
3. \(-9s^{12}+30s^{7}x-25s^{2}x^2=-s^{2}(9s^{10}-30s^5x+25x^2)=-s^{2}(3s^5-5x)^2\)
4. \(-5q^{5}+320q^{3}=-5q^{3}(q^2-64)=-5q^{3}(q+8)(q-8)\)
5. \(-6q^{6}+96q^{4}=-6q^{4}(q^2-16)=-6q^{4}(q+4)(q-4)\)
6. \(98a^{10}+168a^{6}b+72a^{2}b^2=2a^{2}(49a^{8}+84a^4b+36b^2)=2a^{2}(7a^4+6b)^2\)
7. \(-75q^{8}-30q^{6}-3q^{4}=-3q^{4}(25q^{4}+10q^2+1)=-3q^{4}(5q^2+1)^2\)
8. \(-25x^{8}+40x^{5}-16x^{2}=-x^{2}(25x^{6}-40x^3+16)=-x^{2}(5x^3-4)^2\)
9. \(-72y^{13}+98y^{5}=-2y^{5}(36y^{8}-49)=-2y^{5}(6y^4+7)(6y^4-7)\)
10. \(20b^{7}-5b^{5}=5b^{5}(4b^{2}-1)=5b^{5}(2b+1)(2b-1)\)
11. \(-3a^{4}-30a^{3}-75a^{2}=-3a^{2}(a^2+10a+25)=-3a^{2}(a+5)^2\)
12. \(12y^{15}+12y^{10}+3y^{5}=3y^{5}(4y^{10}+4y^5+1)=3y^{5}(2y^5+1)^2\)