Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(q^2+8q+16\)
2. \(b^2+18b+81\)
3. \(p^2+4p+4\)
4. \(x^2-20x+100\)
5. \(225y^2-420y+196\)
6. \(196a^{4}+28a^2+1\)
7. \(100x^2-81b^{4}\)
8. \(64a^{6}-81\)
9. \(169a^{8}-81p^2\)
10. \(81p^{6}-16y^2\)
11. \(25b^2-20b+4\)
12. \(121b^{6}-176b^3p+64p^2\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(q^2+8q+16=(q+4)^2\)
2. \(b^2+18b+81=(b+9)^2\)
3. \(p^2+4p+4=(p+2)^2\)
4. \(x^2-20x+100=(x-10)^2\)
5. \(225y^2-420y+196=(15y-14)^2\)
6. \(196a^{4}+28a^2+1=(14a^2+1)^2\)
7. \(100x^2-81b^{4}=(10x-9b^2)(10x+9b^2)\)
8. \(64a^{6}-81=(8a^3+9)(8a^3-9)\)
9. \(169a^{8}-81p^2=(13a^4+9p)(13a^4-9p)\)
10. \(81p^{6}-16y^2=(9p^3+4y)(9p^3-4y)\)
11. \(25b^2-20b+4=(5b-2)^2\)
12. \(121b^{6}-176b^3p+64p^2=(11b^3-8p)^2\)