Ontbinden in factoren (2)

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

1. \(-36y^{5}+49y^{3}\)
2. \(-25q^{12}-10q^{7}x-q^{2}x^2\)
3. \(-54s^{12}+180s^{7}x-150s^{2}x^2\)
4. \(-180b^{13}+300b^{9}-125b^{5}\)
5. \(50b^{7}-98b^{5}\)
6. \(9a^{5}-16a^{3}\)
7. \(36a^{15}-49a^{5}\)
8. \(-27a^{12}+48a^{4}\)
9. \(12q^{17}-27q^{3}\)
10. \(64q^{7}+16q^{6}+q^{5}\)
11. \(-12y^{19}+3y^{3}\)
12. \(96x^{9}-6x^{5}\)

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

Verbetersleutel

1. \(-36y^{5}+49y^{3}=-y^{3}(36y^{2}-49)=-y^{3}(6y+7)(6y-7)\)
2. \(-25q^{12}-10q^{7}x-q^{2}x^2=-q^{2}(25q^{10}+10q^5x+x^2)=-q^{2}(5q^5+x)^2\)
3. \(-54s^{12}+180s^{7}x-150s^{2}x^2=-6s^{2}(9s^{10}-30s^5x+25x^2)=-6s^{2}(3s^5-5x)^2\)
4. \(-180b^{13}+300b^{9}-125b^{5}=-5b^{5}(36b^{8}-60b^4+25)=-5b^{5}(6b^4-5)^2\)
5. \(50b^{7}-98b^{5}=2b^{5}(25b^{2}-49)=2b^{5}(5b+7)(5b-7)\)
6. \(9a^{5}-16a^{3}=a^{3}(9a^{2}-16)=a^{3}(3a+4)(3a-4)\)
7. \(36a^{15}-49a^{5}=a^{5}(36a^{10}-49)=a^{5}(6a^5+7)(6a^5-7)\)
8. \(-27a^{12}+48a^{4}=-3a^{4}(9a^{8}-16)=-3a^{4}(3a^4+4)(3a^4-4)\)
9. \(12q^{17}-27q^{3}=3q^{3}(4q^{14}-9)=3q^{3}(2q^7+3)(2q^7-3)\)
10. \(64q^{7}+16q^{6}+q^{5}=q^{5}(64q^{2}+16q+1)=q^{5}(8q+1)^2\)
11. \(-12y^{19}+3y^{3}=-3y^{3}(4y^{16}-1)=-3y^{3}(2y^8+1)(2y^8-1)\)
12. \(96x^{9}-6x^{5}=6x^{5}(16x^{4}-1)=6x^{5}(4x^2+1)(4x^2-1)\)