Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(169-36p^{16}\)
2. \(36y^{4}+12y^2+1\)
3. \(256p^{8}-288p^4q+81q^2\)
4. \(100x^{6}-60x^3+9\)
5. \(s^2+20s+100\)
6. \(4a^2+4a+1\)
7. \(a^2+24a+144\)
8. \(100y^2-60y+9\)
9. \(p^2-49\)
10. \(9a^{6}+78a^3s+169s^2\)
11. \(y^2-64\)
12. \(169a^2+260a+100\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(169-36p^{16}=(13-6p^8)(13+6p^8)\)
2. \(36y^{4}+12y^2+1=(6y^2+1)^2\)
3. \(256p^{8}-288p^4q+81q^2=(16p^4-9q)^2\)
4. \(100x^{6}-60x^3+9=(10x^3-3)^2\)
5. \(s^2+20s+100=(s+10)^2\)
6. \(4a^2+4a+1=(2a+1)^2\)
7. \(a^2+24a+144=(a+12)^2\)
8. \(100y^2-60y+9=(10y-3)^2\)
9. \(p^2-49=(p+7)(p-7)\)
10. \(9a^{6}+78a^3s+169s^2=(3a^3+13s)^2\)
11. \(y^2-64=(y-8)(y+8)\)
12. \(169a^2+260a+100=(13a+10)^2\)