Ontbinden in factoren (2)

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

1. \(128p^{12}-224p^{8}y+98p^{4}y^2\)
2. \(-2p^{5}+128p^{3}\)
3. \(27y^{7}-48y^{5}\)
4. \(72p^{13}-120p^{9}x+50p^{5}x^2\)
5. \(p^{5}+6p^{4}+9p^{3}\)
6. \(-48p^{13}-72p^{8}x-27p^{3}x^2\)
7. \(-9a^{17}+4a^{5}\)
8. \(150q^{6}-294q^{4}\)
9. \(-5x^{5}+5x^{3}\)
10. \(5x^{4}-20x^{2}\)
11. \(-6x^{5}+12x^{4}-6x^{3}\)
12. \(2a^{5}-8a^{3}\)

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

Verbetersleutel

1. \(128p^{12}-224p^{8}y+98p^{4}y^2=2p^{4}(64p^{8}-112p^4y+49y^2)=2p^{4}(8p^4-7y)^2\)
2. \(-2p^{5}+128p^{3}=-2p^{3}(p^2-64)=-2p^{3}(p-8)(p+8)\)
3. \(27y^{7}-48y^{5}=3y^{5}(9y^{2}-16)=3y^{5}(3y+4)(3y-4)\)
4. \(72p^{13}-120p^{9}x+50p^{5}x^2=2p^{5}(36p^{8}-60p^4x+25x^2)=2p^{5}(6p^4-5x)^2\)
5. \(p^{5}+6p^{4}+9p^{3}=p^{3}(p^2+6p+9)=p^{3}(p+3)^2\)
6. \(-48p^{13}-72p^{8}x-27p^{3}x^2=-3p^{3}(16p^{10}+24p^5x+9x^2)=-3p^{3}(4p^5+3x)^2\)
7. \(-9a^{17}+4a^{5}=-a^{5}(9a^{12}-4)=-a^{5}(3a^6+2)(3a^6-2)\)
8. \(150q^{6}-294q^{4}=6q^{4}(25q^{2}-49)=6q^{4}(5q+7)(5q-7)\)
9. \(-5x^{5}+5x^{3}=-5x^{3}(x^2-1)=-5x^{3}(x-1)(x+1)\)
10. \(5x^{4}-20x^{2}=5x^{2}(x^2-4)=5x^{2}(x+2)(x-2)\)
11. \(-6x^{5}+12x^{4}-6x^{3}=-6x^{3}(x^2-2x+1)=-6x^{3}(x-1)^2\)
12. \(2a^{5}-8a^{3}=2a^{3}(a^2-4)=2a^{3}(a+2)(a-2)\)