Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(36a^{8}+12a^4q+1q^2\)
2. \(-16a^2+9\)
3. \(b^2+28b+196\)
4. \(225p^{10}-330p^5q+121q^2\)
5. \(-100x^2+1\)
6. \(25b^{8}+10b^4p+1p^2\)
7. \(169q^{14}-16y^2\)
8. \(225y^2-64s^{8}\)
9. \(a^2-25\)
10. \(p^2-81\)
11. \(p^2-169\)
12. \(49y^2-225a^{14}\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(36a^{8}+12a^4q+1q^2=(6a^4+q)^2\)
2. \(-16a^2+9=(3-4a)(3+4a)\)
3. \(b^2+28b+196=(b+14)^2\)
4. \(225p^{10}-330p^5q+121q^2=(15p^5-11q)^2\)
5. \(-100x^2+1=(1-10x)(1+10x)\)
6. \(25b^{8}+10b^4p+1p^2=(5b^4+p)^2\)
7. \(169q^{14}-16y^2=(13q^7+4y)(13q^7-4y)\)
8. \(225y^2-64s^{8}=(15y-8s^4)(15y+8s^4)\)
9. \(a^2-25=(a-5)(a+5)\)
10. \(p^2-81=(p+9)(p-9)\)
11. \(p^2-169=(p-13)(p+13)\)
12. \(49y^2-225a^{14}=(7y-15a^7)(7y+15a^7)\)