Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(100y^{4}-180y^2+81\)
2. \(121x^{4}+286x^2y+169y^2\)
3. \(36a^{4}-60a^2+25\)
4. \(16a^2-56a+49\)
5. \(-225a^2+1\)
6. \(256q^2-225\)
7. \(b^2-49\)
8. \(-121x^2+49\)
9. \(49y^2+154y+121\)
10. \(p^2+18p+81\)
11. \(49q^2-100p^{16}\)
12. \(64q^{4}+176q^2+121\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(100y^{4}-180y^2+81=(10y^2-9)^2\)
2. \(121x^{4}+286x^2y+169y^2=(11x^2+13y)^2\)
3. \(36a^{4}-60a^2+25=(6a^2-5)^2\)
4. \(16a^2-56a+49=(4a-7)^2\)
5. \(-225a^2+1=(1-15a)(1+15a)\)
6. \(256q^2-225=(16q+15)(16q-15)\)
7. \(b^2-49=(b+7)(b-7)\)
8. \(-121x^2+49=(7-11x)(7+11x)\)
9. \(49y^2+154y+121=(7y+11)^2\)
10. \(p^2+18p+81=(p+9)^2\)
11. \(49q^2-100p^{16}=(7q-10p^8)(7q+10p^8)\)
12. \(64q^{4}+176q^2+121=(8q^2+11)^2\)