Ontbinden in factoren (2)

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

1. \(12q^{6}+12q^{4}s+3q^{2}s^2\)
2. \(5q^{4}-10q^{3}+5q^{2}\)
3. \(49y^{7}+14y^{6}+y^{5}\)
4. \(50q^{6}+80q^{5}+32q^{4}\)
5. \(-320x^{5}-560x^{4}-245x^{3}\)
6. \(-a^{6}+25a^{4}\)
7. \(72s^{7}+24s^{6}+2s^{5}\)
8. \(180b^{6}-5b^{2}\)
9. \(-16b^{7}+56b^{6}-49b^{5}\)
10. \(125y^{14}-320y^{4}\)
11. \(-216x^{19}+294x^{5}\)
12. \(150x^{5}-294x^{3}\)

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

Verbetersleutel

1. \(12q^{6}+12q^{4}s+3q^{2}s^2=3q^{2}(4q^{4}+4q^2s+s^2)=3q^{2}(2q^2+s)^2\)
2. \(5q^{4}-10q^{3}+5q^{2}=5q^{2}(q^2-2q+1)=5q^{2}(q-1)^2\)
3. \(49y^{7}+14y^{6}+y^{5}=y^{5}(49y^{2}+14y+1)=y^{5}(7y+1)^2\)
4. \(50q^{6}+80q^{5}+32q^{4}=2q^{4}(25q^{2}+40q+16)=2q^{4}(5q+4)^2\)
5. \(-320x^{5}-560x^{4}-245x^{3}=-5x^{3}(64x^{2}+112x+49)=-5x^{3}(8x+7)^2\)
6. \(-a^{6}+25a^{4}=-a^{4}(a^2-25)=-a^{4}(a+5)(a-5)\)
7. \(72s^{7}+24s^{6}+2s^{5}=2s^{5}(36s^{2}+12s+1)=2s^{5}(6s+1)^2\)
8. \(180b^{6}-5b^{2}=5b^{2}(36b^{4}-1)=5b^{2}(6b^2+1)(6b^2-1)\)
9. \(-16b^{7}+56b^{6}-49b^{5}=-b^{5}(16b^{2}-56b+49)=-b^{5}(4b-7)^2\)
10. \(125y^{14}-320y^{4}=5y^{4}(25y^{10}-64)=5y^{4}(5y^5+8)(5y^5-8)\)
11. \(-216x^{19}+294x^{5}=-6x^{5}(36x^{14}-49)=-6x^{5}(6x^7+7)(6x^7-7)\)
12. \(150x^{5}-294x^{3}=6x^{3}(25x^{2}-49)=6x^{3}(5x+7)(5x-7)\)