Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(196b^{6}-364b^3+169\)
2. \(p^2+18p+81\)
3. \(x^2-6x+9\)
4. \(9b^{4}-16x^2\)
5. \(36b^{14}-49q^2\)
6. \(25-64x^{4}\)
7. \(81q^{10}-198q^5x+121x^2\)
8. \(16b^2-24b+9\)
9. \(-225a^2+169\)
10. \(a^2+14a+49\)
11. \(100p^{4}-60p^2+9\)
12. \(25y^{6}+20y^3+4\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(196b^{6}-364b^3+169=(14b^3-13)^2\)
2. \(p^2+18p+81=(p+9)^2\)
3. \(x^2-6x+9=(x-3)^2\)
4. \(9b^{4}-16x^2=(3b^2+4x)(3b^2-4x)\)
5. \(36b^{14}-49q^2=(6b^7+7q)(6b^7-7q)\)
6. \(25-64x^{4}=(5-8x^2)(5+8x^2)\)
7. \(81q^{10}-198q^5x+121x^2=(9q^5-11x)^2\)
8. \(16b^2-24b+9=(4b-3)^2\)
9. \(-225a^2+169=(13-15a)(13+15a)\)
10. \(a^2+14a+49=(a+7)^2\)
11. \(100p^{4}-60p^2+9=(10p^2-3)^2\)
12. \(25y^{6}+20y^3+4=(5y^3+2)^2\)