Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(225a^{16}-16p^2\)
2. \(-196a^2+225\)
3. \(a^2-9\)
4. \(4a^{4}+28a^2x+49x^2\)
5. \(-256a^2+169\)
6. \(16q^{6}+120q^3+225\)
7. \(169b^{10}-312b^5y+144y^2\)
8. \(225a^{8}+390a^4s+169s^2\)
9. \(p^2+20p+100\)
10. \(x^2-144\)
11. \(121y^2-144q^{16}\)
12. \(9-16y^{10}\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(225a^{16}-16p^2=(15a^8+4p)(15a^8-4p)\)
2. \(-196a^2+225=(15-14a)(15+14a)\)
3. \(a^2-9=(a+3)(a-3)\)
4. \(4a^{4}+28a^2x+49x^2=(2a^2+7x)^2\)
5. \(-256a^2+169=(13-16a)(13+16a)\)
6. \(16q^{6}+120q^3+225=(4q^3+15)^2\)
7. \(169b^{10}-312b^5y+144y^2=(13b^5-12y)^2\)
8. \(225a^{8}+390a^4s+169s^2=(15a^4+13s)^2\)
9. \(p^2+20p+100=(p+10)^2\)
10. \(x^2-144=(x-12)(x+12)\)
11. \(121y^2-144q^{16}=(11y-12q^8)(11y+12q^8)\)
12. \(9-16y^{10}=(3-4y^5)(3+4y^5)\)