Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(256b^{8}+160b^4p+25p^2\)
2. \(81b^{4}-234b^2q+169q^2\)
3. \(169y^{10}+78y^5+9\)
4. \(4a^{6}+4a^3q+1q^2\)
5. \(256a^{8}-480a^4+225\)
6. \(256x^2-25\)
7. \(121y^2-256p^{10}\)
8. \(121x^{14}-144\)
9. \(196x^{6}-252x^3+81\)
10. \(p^2-6p+9\)
11. \(225a^2-420a+196\)
12. \(a^2-25\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(256b^{8}+160b^4p+25p^2=(16b^4+5p)^2\)
2. \(81b^{4}-234b^2q+169q^2=(9b^2-13q)^2\)
3. \(169y^{10}+78y^5+9=(13y^5+3)^2\)
4. \(4a^{6}+4a^3q+1q^2=(2a^3+q)^2\)
5. \(256a^{8}-480a^4+225=(16a^4-15)^2\)
6. \(256x^2-25=(16x+5)(16x-5)\)
7. \(121y^2-256p^{10}=(11y-16p^5)(11y+16p^5)\)
8. \(121x^{14}-144=(11x^7+12)(11x^7-12)\)
9. \(196x^{6}-252x^3+81=(14x^3-9)^2\)
10. \(p^2-6p+9=(p-3)^2\)
11. \(225a^2-420a+196=(15a-14)^2\)
12. \(a^2-25=(a+5)(a-5)\)