Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(16a^{8}+56a^4y+49y^2\)
2. \(144s^{6}-264s^3x+121x^2\)
3. \(225b^2-420b+196\)
4. \(256q^{4}-96q^2+9\)
5. \(49a^{8}-36y^2\)
6. \(100p^{4}+20p^2+1\)
7. \(49x^2-100p^{12}\)
8. \(225s^2-196a^{6}\)
9. \(-81b^2+4\)
10. \(4x^{4}+36x^2+81\)
11. \(-196s^2+81\)
12. \(169-196b^{16}\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(16a^{8}+56a^4y+49y^2=(4a^4+7y)^2\)
2. \(144s^{6}-264s^3x+121x^2=(12s^3-11x)^2\)
3. \(225b^2-420b+196=(15b-14)^2\)
4. \(256q^{4}-96q^2+9=(16q^2-3)^2\)
5. \(49a^{8}-36y^2=(7a^4+6y)(7a^4-6y)\)
6. \(100p^{4}+20p^2+1=(10p^2+1)^2\)
7. \(49x^2-100p^{12}=(7x-10p^6)(7x+10p^6)\)
8. \(225s^2-196a^{6}=(15s-14a^3)(15s+14a^3)\)
9. \(-81b^2+4=(2-9b)(2+9b)\)
10. \(4x^{4}+36x^2+81=(2x^2+9)^2\)
11. \(-196s^2+81=(9-14s)(9+14s)\)
12. \(169-196b^{16}=(13-14b^8)(13+14b^8)\)