Ontbinden in factoren (2)

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

1. \(48y^{5}-27y^{3}\)
2. \(a^{4}-16a^{2}\)
3. \(147a^{6}-252a^{4}+108a^{2}\)
4. \(-45b^{4}-120b^{3}-80b^{2}\)
5. \(75y^{6}-27y^{4}\)
6. \(54q^{11}+144q^{7}+96q^{3}\)
7. \(-x^{4}+14x^{3}-49x^{2}\)
8. \(-49x^{13}-14x^{8}-x^{3}\)
9. \(32a^{8}+48a^{5}+18a^{2}\)
10. \(147b^{11}+126b^{8}+27b^{5}\)
11. \(18a^{7}+48a^{5}+32a^{3}\)
12. \(2x^{6}-18x^{4}\)

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

Verbetersleutel

1. \(48y^{5}-27y^{3}=3y^{3}(16y^{2}-9)=3y^{3}(4y+3)(4y-3)\)
2. \(a^{4}-16a^{2}=a^{2}(a^2-16)=a^{2}(a+4)(a-4)\)
3. \(147a^{6}-252a^{4}+108a^{2}=3a^{2}(49a^{4}-84a^2+36)=3a^{2}(7a^2-6)^2\)
4. \(-45b^{4}-120b^{3}-80b^{2}=-5b^{2}(9b^{2}+24b+16)=-5b^{2}(3b+4)^2\)
5. \(75y^{6}-27y^{4}=3y^{4}(25y^{2}-9)=3y^{4}(5y+3)(5y-3)\)
6. \(54q^{11}+144q^{7}+96q^{3}=6q^{3}(9q^{8}+24q^4+16)=6q^{3}(3q^4+4)^2\)
7. \(-x^{4}+14x^{3}-49x^{2}=-x^{2}(x^2-14x+49)=-x^{2}(x-7)^2\)
8. \(-49x^{13}-14x^{8}-x^{3}=-x^{3}(49x^{10}+14x^5+1)=-x^{3}(7x^5+1)^2\)
9. \(32a^{8}+48a^{5}+18a^{2}=2a^{2}(16a^{6}+24a^3+9)=2a^{2}(4a^3+3)^2\)
10. \(147b^{11}+126b^{8}+27b^{5}=3b^{5}(49b^{6}+42b^3+9)=3b^{5}(7b^3+3)^2\)
11. \(18a^{7}+48a^{5}+32a^{3}=2a^{3}(9a^{4}+24a^2+16)=2a^{3}(3a^2+4)^2\)
12. \(2x^{6}-18x^{4}=2x^{4}(x^2-9)=2x^{4}(x+3)(x-3)\)