Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(y^2+30y+225\)
2. \(121x^{4}-220x^2y+100y^2\)
3. \(25b^2-144a^{16}\)
4. \(49-225p^{4}\)
5. \(25b^2-40b+16\)
6. \(49b^{10}-144x^2\)
7. \(-225a^2+169\)
8. \(25p^{4}+40p^2+16\)
9. \(144q^2-169\)
10. \(169y^2-25q^{4}\)
11. \(y^2+14y+49\)
12. \(196q^{4}-25x^2\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(y^2+30y+225=(y+15)^2\)
2. \(121x^{4}-220x^2y+100y^2=(11x^2-10y)^2\)
3. \(25b^2-144a^{16}=(5b-12a^8)(5b+12a^8)\)
4. \(49-225p^{4}=(7-15p^2)(7+15p^2)\)
5. \(25b^2-40b+16=(5b-4)^2\)
6. \(49b^{10}-144x^2=(7b^5+12x)(7b^5-12x)\)
7. \(-225a^2+169=(13-15a)(13+15a)\)
8. \(25p^{4}+40p^2+16=(5p^2+4)^2\)
9. \(144q^2-169=(12q+13)(12q-13)\)
10. \(169y^2-25q^{4}=(13y-5q^2)(13y+5q^2)\)
11. \(y^2+14y+49=(y+7)^2\)
12. \(196q^{4}-25x^2=(14q^2+5x)(14q^2-5x)\)