Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(196p^{4}+252p^2+81\)
2. \(196q^{10}+420q^5y+225y^2\)
3. \(x^2-18x+81\)
4. \(81a^{6}-234a^3s+169s^2\)
5. \(9-256p^{6}\)
6. \(25a^{6}+130a^3+169\)
7. \(b^2-100\)
8. \(49s^2-42s+9\)
9. \(-36x^2+121\)
10. \(49q^2-9\)
11. \(64q^{16}-25\)
12. \(25a^2-140a+196\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(196p^{4}+252p^2+81=(14p^2+9)^2\)
2. \(196q^{10}+420q^5y+225y^2=(14q^5+15y)^2\)
3. \(x^2-18x+81=(x-9)^2\)
4. \(81a^{6}-234a^3s+169s^2=(9a^3-13s)^2\)
5. \(9-256p^{6}=(3-16p^3)(3+16p^3)\)
6. \(25a^{6}+130a^3+169=(5a^3+13)^2\)
7. \(b^2-100=(b+10)(b-10)\)
8. \(49s^2-42s+9=(7s-3)^2\)
9. \(-36x^2+121=(11-6x)(11+6x)\)
10. \(49q^2-9=(7q+3)(7q-3)\)
11. \(64q^{16}-25=(8q^8+5)(8q^8-5)\)
12. \(25a^2-140a+196=(5a-14)^2\)