Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(225q^2-49a^{6}\)
2. \(36a^{4}-121s^2\)
3. \(x^2-100\)
4. \(169x^2-225a^{16}\)
5. \(36y^2-132y+121\)
6. \(1-100p^{6}\)
7. \(256q^{8}+480q^4x+225x^2\)
8. \(100s^2+180s+81\)
9. \(196s^{14}-81\)
10. \(25a^{10}+90a^5q+81q^2\)
11. \(49-64p^{6}\)
12. \(p^2-225\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(225q^2-49a^{6}=(15q-7a^3)(15q+7a^3)\)
2. \(36a^{4}-121s^2=(6a^2+11s)(6a^2-11s)\)
3. \(x^2-100=(x-10)(x+10)\)
4. \(169x^2-225a^{16}=(13x-15a^8)(13x+15a^8)\)
5. \(36y^2-132y+121=(6y-11)^2\)
6. \(1-100p^{6}=(1-10p^3)(1+10p^3)\)
7. \(256q^{8}+480q^4x+225x^2=(16q^4+15x)^2\)
8. \(100s^2+180s+81=(10s+9)^2\)
9. \(196s^{14}-81=(14s^7+9)(14s^7-9)\)
10. \(25a^{10}+90a^5q+81q^2=(5a^5+9q)^2\)
11. \(49-64p^{6}=(7-8p^3)(7+8p^3)\)
12. \(p^2-225=(p+15)(p-15)\)