Ontbinden in factoren (2)

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

1. \(p^{6}-4p^{4}\)
2. \(5q^{4}+10q^{3}+5q^{2}\)
3. \(-25a^{4}+49a^{2}\)
4. \(-36b^{11}-12b^{7}q-b^{3}q^2\)
5. \(a^{7}-16a^{5}\)
6. \(-320x^{13}+560x^{9}-245x^{5}\)
7. \(-3x^{4}+48x^{2}\)
8. \(9p^{11}-16p^{3}\)
9. \(-8p^{4}+18p^{2}\)
10. \(-2a^{6}+128a^{4}\)
11. \(2q^{6}-98q^{4}\)
12. \(108q^{4}-180q^{3}+75q^{2}\)

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

Verbetersleutel

1. \(p^{6}-4p^{4}=p^{4}(p^2-4)=p^{4}(p+2)(p-2)\)
2. \(5q^{4}+10q^{3}+5q^{2}=5q^{2}(q^2+2q+1)=5q^{2}(q+1)^2\)
3. \(-25a^{4}+49a^{2}=-a^{2}(25a^{2}-49)=-a^{2}(5a+7)(5a-7)\)
4. \(-36b^{11}-12b^{7}q-b^{3}q^2=-b^{3}(36b^{8}+12b^4q+q^2)=-b^{3}(6b^4+q)^2\)
5. \(a^{7}-16a^{5}=a^{5}(a^2-16)=a^{5}(a-4)(a+4)\)
6. \(-320x^{13}+560x^{9}-245x^{5}=-5x^{5}(64x^{8}-112x^4+49)=-5x^{5}(8x^4-7)^2\)
7. \(-3x^{4}+48x^{2}=-3x^{2}(x^2-16)=-3x^{2}(x+4)(x-4)\)
8. \(9p^{11}-16p^{3}=p^{3}(9p^{8}-16)=p^{3}(3p^4+4)(3p^4-4)\)
9. \(-8p^{4}+18p^{2}=-2p^{2}(4p^{2}-9)=-2p^{2}(2p+3)(2p-3)\)
10. \(-2a^{6}+128a^{4}=-2a^{4}(a^2-64)=-2a^{4}(a+8)(a-8)\)
11. \(2q^{6}-98q^{4}=2q^{4}(q^2-49)=2q^{4}(q-7)(q+7)\)
12. \(108q^{4}-180q^{3}+75q^{2}=3q^{2}(36q^{2}-60q+25)=3q^{2}(6q-5)^2\)