Ontbinden in factoren (2)

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

1. \(3y^{7}-27y^{5}\)
2. \(-32x^{6}-80x^{5}-50x^{4}\)
3. \(-75x^{7}+48x^{5}\)
4. \(-25q^{9}+q^{5}\)
5. \(36b^{14}+12b^{9}+b^{4}\)
6. \(18y^{6}-2y^{2}\)
7. \(-3s^{5}+192s^{3}\)
8. \(36s^{12}+60s^{7}+25s^{2}\)
9. \(24x^{10}+24x^{6}y+6x^{2}y^2\)
10. \(-54q^{11}-36q^{7}s-6q^{3}s^2\)
11. \(192x^{10}+240x^{6}+75x^{2}\)
12. \(-3s^{7}+75s^{5}\)

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

Verbetersleutel

1. \(3y^{7}-27y^{5}=3y^{5}(y^2-9)=3y^{5}(y+3)(y-3)\)
2. \(-32x^{6}-80x^{5}-50x^{4}=-2x^{4}(16x^{2}+40x+25)=-2x^{4}(4x+5)^2\)
3. \(-75x^{7}+48x^{5}=-3x^{5}(25x^{2}-16)=-3x^{5}(5x+4)(5x-4)\)
4. \(-25q^{9}+q^{5}=-q^{5}(25q^{4}-1)=-q^{5}(5q^2+1)(5q^2-1)\)
5. \(36b^{14}+12b^{9}+b^{4}=b^{4}(36b^{10}+12b^5+1)=b^{4}(6b^5+1)^2\)
6. \(18y^{6}-2y^{2}=2y^{2}(9y^{4}-1)=2y^{2}(3y^2+1)(3y^2-1)\)
7. \(-3s^{5}+192s^{3}=-3s^{3}(s^2-64)=-3s^{3}(s+8)(s-8)\)
8. \(36s^{12}+60s^{7}+25s^{2}=s^{2}(36s^{10}+60s^5+25)=s^{2}(6s^5+5)^2\)
9. \(24x^{10}+24x^{6}y+6x^{2}y^2=6x^{2}(4x^{8}+4x^4y+y^2)=6x^{2}(2x^4+y)^2\)
10. \(-54q^{11}-36q^{7}s-6q^{3}s^2=-6q^{3}(9q^{8}+6q^4s+s^2)=-6q^{3}(3q^4+s)^2\)
11. \(192x^{10}+240x^{6}+75x^{2}=3x^{2}(64x^{8}+80x^4+25)=3x^{2}(8x^4+5)^2\)
12. \(-3s^{7}+75s^{5}=-3s^{5}(s^2-25)=-3s^{5}(s-5)(s+5)\)