Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(25a^{4}-90a^2x+81x^2\)
2. \(-81q^2+121\)
3. \(196b^{4}+420b^2q+225q^2\)
4. \(196x^{4}-252x^2+81\)
5. \(25y^2-144b^{6}\)
6. \(y^2+4y+4\)
7. \(169a^{6}+260a^3+100\)
8. \(16a^{6}-169x^2\)
9. \(-196a^2+121\)
10. \(-49q^2+81\)
11. \(121-144b^{6}\)
12. \(9b^{4}+6b^2+1\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(25a^{4}-90a^2x+81x^2=(5a^2-9x)^2\)
2. \(-81q^2+121=(11-9q)(11+9q)\)
3. \(196b^{4}+420b^2q+225q^2=(14b^2+15q)^2\)
4. \(196x^{4}-252x^2+81=(14x^2-9)^2\)
5. \(25y^2-144b^{6}=(5y-12b^3)(5y+12b^3)\)
6. \(y^2+4y+4=(y+2)^2\)
7. \(169a^{6}+260a^3+100=(13a^3+10)^2\)
8. \(16a^{6}-169x^2=(4a^3+13x)(4a^3-13x)\)
9. \(-196a^2+121=(11-14a)(11+14a)\)
10. \(-49q^2+81=(9-7q)(9+7q)\)
11. \(121-144b^{6}=(11-12b^3)(11+12b^3)\)
12. \(9b^{4}+6b^2+1=(3b^2+1)^2\)