Ontbinden in factoren (2)

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

1. \(45y^{5}+30y^{4}+5y^{3}\)
2. \(-12b^{6}-36b^{5}-27b^{4}\)
3. \(216b^{14}+72b^{9}y+6b^{4}y^2\)
4. \(-4b^{9}-4b^{7}q-b^{5}q^2\)
5. \(-72x^{11}+50x^{5}\)
6. \(2x^{4}-32x^{2}\)
7. \(6y^{7}+84y^{6}+294y^{5}\)
8. \(-18b^{11}+60b^{8}y-50b^{5}y^2\)
9. \(294a^{12}-252a^{8}+54a^{4}\)
10. \(75x^{6}-108x^{4}\)
11. \(-4x^{4}-4x^{3}-x^{2}\)
12. \(108q^{4}-3q^{2}\)

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

Verbetersleutel

1. \(45y^{5}+30y^{4}+5y^{3}=5y^{3}(9y^{2}+6y+1)=5y^{3}(3y+1)^2\)
2. \(-12b^{6}-36b^{5}-27b^{4}=-3b^{4}(4b^{2}+12b+9)=-3b^{4}(2b+3)^2\)
3. \(216b^{14}+72b^{9}y+6b^{4}y^2=6b^{4}(36b^{10}+12b^5y+y^2)=6b^{4}(6b^5+y)^2\)
4. \(-4b^{9}-4b^{7}q-b^{5}q^2=-b^{5}(4b^{4}+4b^2q+q^2)=-b^{5}(2b^2+q)^2\)
5. \(-72x^{11}+50x^{5}=-2x^{5}(36x^{6}-25)=-2x^{5}(6x^3+5)(6x^3-5)\)
6. \(2x^{4}-32x^{2}=2x^{2}(x^2-16)=2x^{2}(x+4)(x-4)\)
7. \(6y^{7}+84y^{6}+294y^{5}=6y^{5}(y^2+14y+49)=6y^{5}(y+7)^2\)
8. \(-18b^{11}+60b^{8}y-50b^{5}y^2=-2b^{5}(9b^{6}-30b^3y+25y^2)=-2b^{5}(3b^3-5y)^2\)
9. \(294a^{12}-252a^{8}+54a^{4}=6a^{4}(49a^{8}-42a^4+9)=6a^{4}(7a^4-3)^2\)
10. \(75x^{6}-108x^{4}=3x^{4}(25x^{2}-36)=3x^{4}(5x+6)(5x-6)\)
11. \(-4x^{4}-4x^{3}-x^{2}=-x^{2}(4x^{2}+4x+1)=-x^{2}(2x+1)^2\)
12. \(108q^{4}-3q^{2}=3q^{2}(36q^{2}-1)=3q^{2}(6q+1)(6q-1)\)