Ontbinden in factoren (2)

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

1. \(-45y^{4}+80y^{2}\)
2. \(-50p^{6}+140p^{5}-98p^{4}\)
3. \(12q^{5}-3q^{3}\)
4. \(32p^{11}-2p^{3}\)
5. \(-12y^{7}+27y^{3}\)
6. \(2a^{4}-72a^{2}\)
7. \(-2a^{6}+32a^{4}\)
8. \(150q^{12}-420q^{7}x+294q^{2}x^2\)
9. \(20y^{8}-245y^{2}\)
10. \(-6a^{5}-96a^{4}-384a^{3}\)
11. \(-2q^{6}-20q^{5}-50q^{4}\)
12. \(5q^{6}-40q^{5}+80q^{4}\)

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

Verbetersleutel

1. \(-45y^{4}+80y^{2}=-5y^{2}(9y^{2}-16)=-5y^{2}(3y+4)(3y-4)\)
2. \(-50p^{6}+140p^{5}-98p^{4}=-2p^{4}(25p^{2}-70p+49)=-2p^{4}(5p-7)^2\)
3. \(12q^{5}-3q^{3}=3q^{3}(4q^{2}-1)=3q^{3}(2q+1)(2q-1)\)
4. \(32p^{11}-2p^{3}=2p^{3}(16p^{8}-1)=2p^{3}(4p^4+1)(4p^4-1)\)
5. \(-12y^{7}+27y^{3}=-3y^{3}(4y^{4}-9)=-3y^{3}(2y^2+3)(2y^2-3)\)
6. \(2a^{4}-72a^{2}=2a^{2}(a^2-36)=2a^{2}(a+6)(a-6)\)
7. \(-2a^{6}+32a^{4}=-2a^{4}(a^2-16)=-2a^{4}(a-4)(a+4)\)
8. \(150q^{12}-420q^{7}x+294q^{2}x^2=6q^{2}(25q^{10}-70q^5x+49x^2)=6q^{2}(5q^5-7x)^2\)
9. \(20y^{8}-245y^{2}=5y^{2}(4y^{6}-49)=5y^{2}(2y^3+7)(2y^3-7)\)
10. \(-6a^{5}-96a^{4}-384a^{3}=-6a^{3}(a^2+16a+64)=-6a^{3}(a+8)^2\)
11. \(-2q^{6}-20q^{5}-50q^{4}=-2q^{4}(q^2+10q+25)=-2q^{4}(q+5)^2\)
12. \(5q^{6}-40q^{5}+80q^{4}=5q^{4}(q^2-8q+16)=5q^{4}(q-4)^2\)