Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(49-225x^{12}\)
2. \(4p^{8}+52p^4+169\)
3. \(4y^{4}+60y^2+225\)
4. \(169-100s^{10}\)
5. \(169q^2-78q+9\)
6. \(64y^{6}-112y^3+49\)
7. \(64y^2+80y+25\)
8. \(9q^2-84q+196\)
9. \(100x^2-60x+9\)
10. \(s^2+22s+121\)
11. \(25b^{10}-16\)
12. \(a^2-121\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(49-225x^{12}=(7-15x^6)(7+15x^6)\)
2. \(4p^{8}+52p^4+169=(2p^4+13)^2\)
3. \(4y^{4}+60y^2+225=(2y^2+15)^2\)
4. \(169-100s^{10}=(13-10s^5)(13+10s^5)\)
5. \(169q^2-78q+9=(13q-3)^2\)
6. \(64y^{6}-112y^3+49=(8y^3-7)^2\)
7. \(64y^2+80y+25=(8y+5)^2\)
8. \(9q^2-84q+196=(3q-14)^2\)
9. \(100x^2-60x+9=(10x-3)^2\)
10. \(s^2+22s+121=(s+11)^2\)
11. \(25b^{10}-16=(5b^5+4)(5b^5-4)\)
12. \(a^2-121=(a-11)(a+11)\)