Ontbinden in factoren (2)

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

1. \(-25s^{6}+16s^{4}\)
2. \(75y^{15}-108y^{5}\)
3. \(16b^{15}-25b^{5}\)
4. \(-125s^{7}+245s^{5}\)
5. \(-2a^{7}+28a^{6}-98a^{5}\)
6. \(2a^{7}-18a^{5}\)
7. \(150x^{4}+240x^{3}+96x^{2}\)
8. \(-2x^{7}-16x^{6}-32x^{5}\)
9. \(b^{4}+6b^{3}+9b^{2}\)
10. \(12p^{10}+12p^{7}+3p^{4}\)
11. \(6b^{6}-150b^{4}\)
12. \(-4p^{11}+9p^{5}\)

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

Verbetersleutel

1. \(-25s^{6}+16s^{4}=-s^{4}(25s^{2}-16)=-s^{4}(5s+4)(5s-4)\)
2. \(75y^{15}-108y^{5}=3y^{5}(25y^{10}-36)=3y^{5}(5y^5+6)(5y^5-6)\)
3. \(16b^{15}-25b^{5}=b^{5}(16b^{10}-25)=b^{5}(4b^5+5)(4b^5-5)\)
4. \(-125s^{7}+245s^{5}=-5s^{5}(25s^{2}-49)=-5s^{5}(5s+7)(5s-7)\)
5. \(-2a^{7}+28a^{6}-98a^{5}=-2a^{5}(a^2-14a+49)=-2a^{5}(a-7)^2\)
6. \(2a^{7}-18a^{5}=2a^{5}(a^2-9)=2a^{5}(a-3)(a+3)\)
7. \(150x^{4}+240x^{3}+96x^{2}=6x^{2}(25x^{2}+40x+16)=6x^{2}(5x+4)^2\)
8. \(-2x^{7}-16x^{6}-32x^{5}=-2x^{5}(x^2+8x+16)=-2x^{5}(x+4)^2\)
9. \(b^{4}+6b^{3}+9b^{2}=b^{2}(b^2+6b+9)=b^{2}(b+3)^2\)
10. \(12p^{10}+12p^{7}+3p^{4}=3p^{4}(4p^{6}+4p^3+1)=3p^{4}(2p^3+1)^2\)
11. \(6b^{6}-150b^{4}=6b^{4}(b^2-25)=6b^{4}(b-5)(b+5)\)
12. \(-4p^{11}+9p^{5}=-p^{5}(4p^{6}-9)=-p^{5}(2p^3+3)(2p^3-3)\)