Ontbinden in factoren (2)

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

1. \(-36a^{12}+25a^{4}\)
2. \(-16y^{6}+9y^{4}\)
3. \(-320y^{12}+560y^{8}-245y^{4}\)
4. \(-16q^{7}+25q^{5}\)
5. \(-125s^{10}-50s^{7}x-5s^{4}x^2\)
6. \(4q^{5}-25q^{3}\)
7. \(-384s^{7}+672s^{6}-294s^{5}\)
8. \(36y^{11}-49y^{5}\)
9. \(-147a^{8}+252a^{5}-108a^{2}\)
10. \(-45x^{12}+150x^{8}-125x^{4}\)
11. \(y^{6}-2y^{5}+y^{4}\)
12. \(-8q^{5}+2q^{3}\)

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

Verbetersleutel

1. \(-36a^{12}+25a^{4}=-a^{4}(36a^{8}-25)=-a^{4}(6a^4+5)(6a^4-5)\)
2. \(-16y^{6}+9y^{4}=-y^{4}(16y^{2}-9)=-y^{4}(4y+3)(4y-3)\)
3. \(-320y^{12}+560y^{8}-245y^{4}=-5y^{4}(64y^{8}-112y^4+49)=-5y^{4}(8y^4-7)^2\)
4. \(-16q^{7}+25q^{5}=-q^{5}(16q^{2}-25)=-q^{5}(4q+5)(4q-5)\)
5. \(-125s^{10}-50s^{7}x-5s^{4}x^2=-5s^{4}(25s^{6}+10s^3x+x^2)=-5s^{4}(5s^3+x)^2\)
6. \(4q^{5}-25q^{3}=q^{3}(4q^{2}-25)=q^{3}(2q+5)(2q-5)\)
7. \(-384s^{7}+672s^{6}-294s^{5}=-6s^{5}(64s^{2}-112s+49)=-6s^{5}(8s-7)^2\)
8. \(36y^{11}-49y^{5}=y^{5}(36y^{6}-49)=y^{5}(6y^3+7)(6y^3-7)\)
9. \(-147a^{8}+252a^{5}-108a^{2}=-3a^{2}(49a^{6}-84a^3+36)=-3a^{2}(7a^3-6)^2\)
10. \(-45x^{12}+150x^{8}-125x^{4}=-5x^{4}(9x^{8}-30x^4+25)=-5x^{4}(3x^4-5)^2\)
11. \(y^{6}-2y^{5}+y^{4}=y^{4}(y^2-2y+1)=y^{4}(y-1)^2\)
12. \(-8q^{5}+2q^{3}=-2q^{3}(4q^{2}-1)=-2q^{3}(2q+1)(2q-1)\)