Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(100x^2-49b^{4}\)
2. \(225s^2-49a^{12}\)
3. \(a^2+18a+81\)
4. \(196q^{4}-252q^2x+81x^2\)
5. \(16p^{10}+120p^5x+225x^2\)
6. \(y^2+28y+196\)
7. \(9p^{4}-16\)
8. \(121-100x^{16}\)
9. \(64x^{8}+208x^4y+169y^2\)
10. \(1-144q^{8}\)
11. \(q^2-6q+9\)
12. \(36a^{10}+12a^5x+1x^2\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(100x^2-49b^{4}=(10x-7b^2)(10x+7b^2)\)
2. \(225s^2-49a^{12}=(15s-7a^6)(15s+7a^6)\)
3. \(a^2+18a+81=(a+9)^2\)
4. \(196q^{4}-252q^2x+81x^2=(14q^2-9x)^2\)
5. \(16p^{10}+120p^5x+225x^2=(4p^5+15x)^2\)
6. \(y^2+28y+196=(y+14)^2\)
7. \(9p^{4}-16=(3p^2+4)(3p^2-4)\)
8. \(121-100x^{16}=(11-10x^8)(11+10x^8)\)
9. \(64x^{8}+208x^4y+169y^2=(8x^4+13y)^2\)
10. \(1-144q^{8}=(1-12q^4)(1+12q^4)\)
11. \(q^2-6q+9=(q-3)^2\)
12. \(36a^{10}+12a^5x+1x^2=(6a^5+x)^2\)