Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(25y^{10}-49\)
2. \(49q^2+14q+1\)
3. \(4s^2-225q^{4}\)
4. \(121b^{8}-220b^4q+100q^2\)
5. \(p^2-4p+4\)
6. \(49q^{4}-224q^2x+256x^2\)
7. \(169a^{12}-144x^2\)
8. \(q^2-26q+169\)
9. \(256s^{4}+288s^2y+81y^2\)
10. \(s^2+30s+225\)
11. \(169a^{10}-416a^5q+256q^2\)
12. \(169q^{8}-390q^4+225\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(25y^{10}-49=(5y^5+7)(5y^5-7)\)
2. \(49q^2+14q+1=(7q+1)^2\)
3. \(4s^2-225q^{4}=(2s-15q^2)(2s+15q^2)\)
4. \(121b^{8}-220b^4q+100q^2=(11b^4-10q)^2\)
5. \(p^2-4p+4=(p-2)^2\)
6. \(49q^{4}-224q^2x+256x^2=(7q^2-16x)^2\)
7. \(169a^{12}-144x^2=(13a^6+12x)(13a^6-12x)\)
8. \(q^2-26q+169=(q-13)^2\)
9. \(256s^{4}+288s^2y+81y^2=(16s^2+9y)^2\)
10. \(s^2+30s+225=(s+15)^2\)
11. \(169a^{10}-416a^5q+256q^2=(13a^5-16q)^2\)
12. \(169q^{8}-390q^4+225=(13q^4-15)^2\)