Ontbinden in factoren (2)

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

1. \(-24y^{5}+6y^{3}\)
2. \(16a^{13}-24a^{9}p+9a^{5}p^2\)
3. \(12p^{5}+84p^{4}+147p^{3}\)
4. \(27b^{10}+72b^{6}q+48b^{2}q^2\)
5. \(72y^{19}-98y^{3}\)
6. \(-294x^{9}+168x^{7}-24x^{5}\)
7. \(96x^{12}-336x^{7}y+294x^{2}y^2\)
8. \(25x^{13}-36x^{5}\)
9. \(9x^{7}-16x^{5}\)
10. \(-2y^{7}+32y^{6}-128y^{5}\)
11. \(45a^{7}+120a^{6}+80a^{5}\)
12. \(-216b^{8}-72b^{6}-6b^{4}\)

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

Verbetersleutel

1. \(-24y^{5}+6y^{3}=-6y^{3}(4y^{2}-1)=-6y^{3}(2y+1)(2y-1)\)
2. \(16a^{13}-24a^{9}p+9a^{5}p^2=a^{5}(16a^{8}-24a^4p+9p^2)=a^{5}(4a^4-3p)^2\)
3. \(12p^{5}+84p^{4}+147p^{3}=3p^{3}(4p^{2}+28p+49)=3p^{3}(2p+7)^2\)
4. \(27b^{10}+72b^{6}q+48b^{2}q^2=3b^{2}(9b^{8}+24b^4q+16q^2)=3b^{2}(3b^4+4q)^2\)
5. \(72y^{19}-98y^{3}=2y^{3}(36y^{16}-49)=2y^{3}(6y^8+7)(6y^8-7)\)
6. \(-294x^{9}+168x^{7}-24x^{5}=-6x^{5}(49x^{4}-28x^2+4)=-6x^{5}(7x^2-2)^2\)
7. \(96x^{12}-336x^{7}y+294x^{2}y^2=6x^{2}(16x^{10}-56x^5y+49y^2)=6x^{2}(4x^5-7y)^2\)
8. \(25x^{13}-36x^{5}=x^{5}(25x^{8}-36)=x^{5}(5x^4+6)(5x^4-6)\)
9. \(9x^{7}-16x^{5}=x^{5}(9x^{2}-16)=x^{5}(3x+4)(3x-4)\)
10. \(-2y^{7}+32y^{6}-128y^{5}=-2y^{5}(y^2-16y+64)=-2y^{5}(y-8)^2\)
11. \(45a^{7}+120a^{6}+80a^{5}=5a^{5}(9a^{2}+24a+16)=5a^{5}(3a+4)^2\)
12. \(-216b^{8}-72b^{6}-6b^{4}=-6b^{4}(36b^{4}+12b^2+1)=-6b^{4}(6b^2+1)^2\)