Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(144s^{4}-168s^2+49\)
2. \(225x^{10}-16\)
3. \(225a^{8}-169p^2\)
4. \(256b^2-288b+81\)
5. \(169b^2-36a^{16}\)
6. \(p^2-20p+100\)
7. \(256b^{8}-225y^2\)
8. \(196x^{4}-364x^2y+169y^2\)
9. \(y^2-16y+64\)
10. \(196p^2+28p+1\)
11. \(-81x^2+1\)
12. \(s^2-169\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(144s^{4}-168s^2+49=(12s^2-7)^2\)
2. \(225x^{10}-16=(15x^5+4)(15x^5-4)\)
3. \(225a^{8}-169p^2=(15a^4+13p)(15a^4-13p)\)
4. \(256b^2-288b+81=(16b-9)^2\)
5. \(169b^2-36a^{16}=(13b-6a^8)(13b+6a^8)\)
6. \(p^2-20p+100=(p-10)^2\)
7. \(256b^{8}-225y^2=(16b^4+15y)(16b^4-15y)\)
8. \(196x^{4}-364x^2y+169y^2=(14x^2-13y)^2\)
9. \(y^2-16y+64=(y-8)^2\)
10. \(196p^2+28p+1=(14p+1)^2\)
11. \(-81x^2+1=(1-9x)(1+9x)\)
12. \(s^2-169=(s+13)(s-13)\)