Ontbinden in factoren (2)

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

1. \(-16a^{11}+25a^{3}\)
2. \(-216a^{5}+150a^{3}\)
3. \(32a^{4}-18a^{2}\)
4. \(18y^{5}-2y^{3}\)
5. \(-20b^{5}+45b^{3}\)
6. \(150x^{4}-6x^{2}\)
7. \(-2y^{7}+32y^{5}\)
8. \(32b^{15}+80b^{10}x+50b^{5}x^2\)
9. \(180x^{8}+300x^{5}y+125x^{2}y^2\)
10. \(75b^{6}-27b^{2}\)
11. \(128b^{10}-224b^{6}x+98b^{2}x^2\)
12. \(a^{4}+10a^{3}+25a^{2}\)

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

Verbetersleutel

1. \(-16a^{11}+25a^{3}=-a^{3}(16a^{8}-25)=-a^{3}(4a^4+5)(4a^4-5)\)
2. \(-216a^{5}+150a^{3}=-6a^{3}(36a^{2}-25)=-6a^{3}(6a+5)(6a-5)\)
3. \(32a^{4}-18a^{2}=2a^{2}(16a^{2}-9)=2a^{2}(4a+3)(4a-3)\)
4. \(18y^{5}-2y^{3}=2y^{3}(9y^{2}-1)=2y^{3}(3y+1)(3y-1)\)
5. \(-20b^{5}+45b^{3}=-5b^{3}(4b^{2}-9)=-5b^{3}(2b+3)(2b-3)\)
6. \(150x^{4}-6x^{2}=6x^{2}(25x^{2}-1)=6x^{2}(5x+1)(5x-1)\)
7. \(-2y^{7}+32y^{5}=-2y^{5}(y^2-16)=-2y^{5}(y-4)(y+4)\)
8. \(32b^{15}+80b^{10}x+50b^{5}x^2=2b^{5}(16b^{10}+40b^5x+25x^2)=2b^{5}(4b^5+5x)^2\)
9. \(180x^{8}+300x^{5}y+125x^{2}y^2=5x^{2}(36x^{6}+60x^3y+25y^2)=5x^{2}(6x^3+5y)^2\)
10. \(75b^{6}-27b^{2}=3b^{2}(25b^{4}-9)=3b^{2}(5b^2+3)(5b^2-3)\)
11. \(128b^{10}-224b^{6}x+98b^{2}x^2=2b^{2}(64b^{8}-112b^4x+49x^2)=2b^{2}(8b^4-7x)^2\)
12. \(a^{4}+10a^{3}+25a^{2}=a^{2}(a^2+10a+25)=a^{2}(a+5)^2\)