Ontbinden in factoren (2)

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

1. \(-p^{4}+p^{2}\)
2. \(-64q^{5}-80q^{4}-25q^{3}\)
3. \(-16x^{15}+24x^{10}y-9x^{5}y^2\)
4. \(384a^{4}+96a^{3}+6a^{2}\)
5. \(-128p^{6}-32p^{4}q-2p^{2}q^2\)
6. \(180s^{5}-125s^{3}\)
7. \(24x^{12}+24x^{8}y+6x^{4}y^2\)
8. \(-48x^{7}+72x^{6}-27x^{5}\)
9. \(32q^{15}-112q^{10}x+98q^{5}x^2\)
10. \(-6x^{6}+96x^{5}-384x^{4}\)
11. \(48q^{6}-147q^{2}\)
12. \(5a^{5}-80a^{3}\)

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

Verbetersleutel

1. \(-p^{4}+p^{2}=-p^{2}(p^2-1)=-p^{2}(p+1)(p-1)\)
2. \(-64q^{5}-80q^{4}-25q^{3}=-q^{3}(64q^{2}+80q+25)=-q^{3}(8q+5)^2\)
3. \(-16x^{15}+24x^{10}y-9x^{5}y^2=-x^{5}(16x^{10}-24x^5y+9y^2)=-x^{5}(4x^5-3y)^2\)
4. \(384a^{4}+96a^{3}+6a^{2}=6a^{2}(64a^{2}+16a+1)=6a^{2}(8a+1)^2\)
5. \(-128p^{6}-32p^{4}q-2p^{2}q^2=-2p^{2}(64p^{4}+16p^2q+q^2)=-2p^{2}(8p^2+q)^2\)
6. \(180s^{5}-125s^{3}=5s^{3}(36s^{2}-25)=5s^{3}(6s+5)(6s-5)\)
7. \(24x^{12}+24x^{8}y+6x^{4}y^2=6x^{4}(4x^{8}+4x^4y+y^2)=6x^{4}(2x^4+y)^2\)
8. \(-48x^{7}+72x^{6}-27x^{5}=-3x^{5}(16x^{2}-24x+9)=-3x^{5}(4x-3)^2\)
9. \(32q^{15}-112q^{10}x+98q^{5}x^2=2q^{5}(16q^{10}-56q^5x+49x^2)=2q^{5}(4q^5-7x)^2\)
10. \(-6x^{6}+96x^{5}-384x^{4}=-6x^{4}(x^2-16x+64)=-6x^{4}(x-8)^2\)
11. \(48q^{6}-147q^{2}=3q^{2}(16q^{4}-49)=3q^{2}(4q^2+7)(4q^2-7)\)
12. \(5a^{5}-80a^{3}=5a^{3}(a^2-16)=5a^{3}(a+4)(a-4)\)