Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(9a^{10}-84a^5p+196p^2\)
2. \(-25b^2+1\)
3. \(169s^2+234s+81\)
4. \(-49a^2+144\)
5. \(49b^{6}-182b^3y+169y^2\)
6. \(a^2-196\)
7. \(q^2-49\)
8. \(49q^{10}-4s^2\)
9. \(s^2-225\)
10. \(25p^{10}-140p^5y+196y^2\)
11. \(64p^{16}-49y^2\)
12. \(64q^{10}-169y^2\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(9a^{10}-84a^5p+196p^2=(3a^5-14p)^2\)
2. \(-25b^2+1=(1-5b)(1+5b)\)
3. \(169s^2+234s+81=(13s+9)^2\)
4. \(-49a^2+144=(12-7a)(12+7a)\)
5. \(49b^{6}-182b^3y+169y^2=(7b^3-13y)^2\)
6. \(a^2-196=(a-14)(a+14)\)
7. \(q^2-49=(q-7)(q+7)\)
8. \(49q^{10}-4s^2=(7q^5+2s)(7q^5-2s)\)
9. \(s^2-225=(s+15)(s-15)\)
10. \(25p^{10}-140p^5y+196y^2=(5p^5-14y)^2\)
11. \(64p^{16}-49y^2=(8p^8+7y)(8p^8-7y)\)
12. \(64q^{10}-169y^2=(8q^5+13y)(8q^5-13y)\)