Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(4s^{8}+4s^4+1\)
2. \(s^2-10s+25\)
3. \(196s^2+252s+81\)
4. \(9x^2-49a^{12}\)
5. \(81q^{4}+36q^2x+4x^2\)
6. \(100a^{10}-81y^2\)
7. \(196y^2-81\)
8. \(4q^2-225\)
9. \(256b^{6}+288b^3q+81q^2\)
10. \(64q^{8}+144q^4y+81y^2\)
11. \(81a^{8}+144a^4p+64p^2\)
12. \(256q^{6}+32q^3+1\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(4s^{8}+4s^4+1=(2s^4+1)^2\)
2. \(s^2-10s+25=(s-5)^2\)
3. \(196s^2+252s+81=(14s+9)^2\)
4. \(9x^2-49a^{12}=(3x-7a^6)(3x+7a^6)\)
5. \(81q^{4}+36q^2x+4x^2=(9q^2+2x)^2\)
6. \(100a^{10}-81y^2=(10a^5+9y)(10a^5-9y)\)
7. \(196y^2-81=(14y+9)(14y-9)\)
8. \(4q^2-225=(2q+15)(2q-15)\)
9. \(256b^{6}+288b^3q+81q^2=(16b^3+9q)^2\)
10. \(64q^{8}+144q^4y+81y^2=(8q^4+9y)^2\)
11. \(81a^{8}+144a^4p+64p^2=(9a^4+8p)^2\)
12. \(256q^{6}+32q^3+1=(16q^3+1)^2\)