Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(p^2-6p+9\)
2. \(225q^{10}+120q^5+16\)
3. \(81q^{10}-16\)
4. \(1-144q^{8}\)
5. \(s^2-8s+16\)
6. \(100s^{6}-260s^3x+169x^2\)
7. \(49x^{8}-224x^4+256\)
8. \(169b^{10}+208b^5+64\)
9. \(49p^{6}+210p^3+225\)
10. \(256x^2-160x+25\)
11. \(-4a^2+225\)
12. \(169x^{12}-4y^2\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(p^2-6p+9=(p-3)^2\)
2. \(225q^{10}+120q^5+16=(15q^5+4)^2\)
3. \(81q^{10}-16=(9q^5+4)(9q^5-4)\)
4. \(1-144q^{8}=(1-12q^4)(1+12q^4)\)
5. \(s^2-8s+16=(s-4)^2\)
6. \(100s^{6}-260s^3x+169x^2=(10s^3-13x)^2\)
7. \(49x^{8}-224x^4+256=(7x^4-16)^2\)
8. \(169b^{10}+208b^5+64=(13b^5+8)^2\)
9. \(49p^{6}+210p^3+225=(7p^3+15)^2\)
10. \(256x^2-160x+25=(16x-5)^2\)
11. \(-4a^2+225=(15-2a)(15+2a)\)
12. \(169x^{12}-4y^2=(13x^6+2y)(13x^6-2y)\)