Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(144q^{6}-264q^3x+121x^2\)
2. \(p^2-16\)
3. \(100p^{10}+220p^5+121\)
4. \(49p^{6}-224p^3y+256y^2\)
5. \(a^2+22a+121\)
6. \(q^2-9\)
7. \(9p^{14}-49x^2\)
8. \(4q^{8}-81x^2\)
9. \(196s^2+252s+81\)
10. \(81x^2-256p^{12}\)
11. \(a^2-6a+9\)
12. \(49a^{10}-225p^2\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(144q^{6}-264q^3x+121x^2=(12q^3-11x)^2\)
2. \(p^2-16=(p+4)(p-4)\)
3. \(100p^{10}+220p^5+121=(10p^5+11)^2\)
4. \(49p^{6}-224p^3y+256y^2=(7p^3-16y)^2\)
5. \(a^2+22a+121=(a+11)^2\)
6. \(q^2-9=(q-3)(q+3)\)
7. \(9p^{14}-49x^2=(3p^7+7x)(3p^7-7x)\)
8. \(4q^{8}-81x^2=(2q^4+9x)(2q^4-9x)\)
9. \(196s^2+252s+81=(14s+9)^2\)
10. \(81x^2-256p^{12}=(9x-16p^6)(9x+16p^6)\)
11. \(a^2-6a+9=(a-3)^2\)
12. \(49a^{10}-225p^2=(7a^5+15p)(7a^5-15p)\)