Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(64q^{6}-81\)
2. \(81b^{6}-72b^3+16\)
3. \(q^2+30q+225\)
4. \(169b^{6}+104b^3+16\)
5. \(100y^{10}-1\)
6. \(q^2+22q+121\)
7. \(9s^2+30s+25\)
8. \(169s^{4}-78s^2y+9y^2\)
9. \(16a^{6}-9s^2\)
10. \(q^2-196\)
11. \(16p^2-56p+49\)
12. \(36x^2-1\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(64q^{6}-81=(8q^3+9)(8q^3-9)\)
2. \(81b^{6}-72b^3+16=(9b^3-4)^2\)
3. \(q^2+30q+225=(q+15)^2\)
4. \(169b^{6}+104b^3+16=(13b^3+4)^2\)
5. \(100y^{10}-1=(10y^5+1)(10y^5-1)\)
6. \(q^2+22q+121=(q+11)^2\)
7. \(9s^2+30s+25=(3s+5)^2\)
8. \(169s^{4}-78s^2y+9y^2=(13s^2-3y)^2\)
9. \(16a^{6}-9s^2=(4a^3+3s)(4a^3-3s)\)
10. \(q^2-196=(q+14)(q-14)\)
11. \(16p^2-56p+49=(4p-7)^2\)
12. \(36x^2-1=(6x+1)(6x-1)\)