Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(9b^2-16a^{12}\)
2. \(64b^{12}-25x^2\)
3. \(81p^{4}+252p^2q+196q^2\)
4. \(64a^2-9\)
5. \(36q^2-132q+121\)
6. \(64a^{8}-240a^4p+225p^2\)
7. \(-49q^2+1\)
8. \(b^2-4\)
9. \(144q^{6}-264q^3s+121s^2\)
10. \(-36q^2+1\)
11. \(q^2-81\)
12. \(25b^{8}-140b^4q+196q^2\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(9b^2-16a^{12}=(3b-4a^6)(3b+4a^6)\)
2. \(64b^{12}-25x^2=(8b^6+5x)(8b^6-5x)\)
3. \(81p^{4}+252p^2q+196q^2=(9p^2+14q)^2\)
4. \(64a^2-9=(8a+3)(8a-3)\)
5. \(36q^2-132q+121=(6q-11)^2\)
6. \(64a^{8}-240a^4p+225p^2=(8a^4-15p)^2\)
7. \(-49q^2+1=(1-7q)(1+7q)\)
8. \(b^2-4=(b+2)(b-2)\)
9. \(144q^{6}-264q^3s+121s^2=(12q^3-11s)^2\)
10. \(-36q^2+1=(1-6q)(1+6q)\)
11. \(q^2-81=(q+9)(q-9)\)
12. \(25b^{8}-140b^4q+196q^2=(5b^4-14q)^2\)