Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(a^2-100\)
2. \(p^2-196\)
3. \(36p^{4}-132p^2+121\)
4. \(25x^2-p^{12}\)
5. \(144p^2-168p+49\)
6. \(64a^{4}-81q^2\)
7. \(100a^{4}+180a^2q+81q^2\)
8. \(4q^{4}-81x^2\)
9. \(169a^2-156a+36\)
10. \(225b^2-330b+121\)
11. \(-36b^2+169\)
12. \(144q^{8}-264q^4y+121y^2\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(a^2-100=(a+10)(a-10)\)
2. \(p^2-196=(p-14)(p+14)\)
3. \(36p^{4}-132p^2+121=(6p^2-11)^2\)
4. \(25x^2-p^{12}=(5x-p^6)(5x+p^6)\)
5. \(144p^2-168p+49=(12p-7)^2\)
6. \(64a^{4}-81q^2=(8a^2+9q)(8a^2-9q)\)
7. \(100a^{4}+180a^2q+81q^2=(10a^2+9q)^2\)
8. \(4q^{4}-81x^2=(2q^2+9x)(2q^2-9x)\)
9. \(169a^2-156a+36=(13a-6)^2\)
10. \(225b^2-330b+121=(15b-11)^2\)
11. \(-36b^2+169=(13-6b)(13+6b)\)
12. \(144q^{8}-264q^4y+121y^2=(12q^4-11y)^2\)