Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(a^2-49\)
2. \(16b^2-9a^{10}\)
3. \(25b^2-196a^{12}\)
4. \(256a^{6}-288a^3y+81y^2\)
5. \(25p^{6}+30p^3y+9y^2\)
6. \(q^2-2q+1\)
7. \(9s^2-256a^{12}\)
8. \(64a^2-225\)
9. \(9s^{6}-30s^3+25\)
10. \(q^2-25\)
11. \(b^2-22b+121\)
12. \(b^{14}-16q^2\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(a^2-49=(a+7)(a-7)\)
2. \(16b^2-9a^{10}=(4b-3a^5)(4b+3a^5)\)
3. \(25b^2-196a^{12}=(5b-14a^6)(5b+14a^6)\)
4. \(256a^{6}-288a^3y+81y^2=(16a^3-9y)^2\)
5. \(25p^{6}+30p^3y+9y^2=(5p^3+3y)^2\)
6. \(q^2-2q+1=(q-1)^2\)
7. \(9s^2-256a^{12}=(3s-16a^6)(3s+16a^6)\)
8. \(64a^2-225=(8a+15)(8a-15)\)
9. \(9s^{6}-30s^3+25=(3s^3-5)^2\)
10. \(q^2-25=(q-5)(q+5)\)
11. \(b^2-22b+121=(b-11)^2\)
12. \(b^{14}-16q^2=(b^7+4q)(b^7-4q)\)